Klitschko, who shares a daughter with Panettiere, remembered the Heroes and Nashville star for her "immense talent" following her death on Sunday at the age of 36.
The actress was found in her home in Greenville, South Carolina, by police, following reports that she was "unresponsive" and in "cardiac arrest".
The cause and manner of her death have not been confirmed, but police said there were "no signs of foul play or suspicious circumstances".
Klitschko and Panettiere were together from 2009 to 2018, and their daughter was born in 2014.
The Ukrainian heavyweight champion wrote on Instagram: "Our family is going through a time of profound shock and grief.
"The announcement of Hayden's tragic death saddens me deeply.
"She left this world far too soon.
"Hayden was, although no longer my partner, an important part of my life and the mother of our daughter, Kaya."
In 2018, Panettiere relinquished full custody to Klitschko as she struggled with addiction and mental health.
Panettiere was a child actress before rocketing to fame in the TV show Heroes. She also starred in films, including 2006's Bring It On: All Or Nothing, comedy-drama film Raising Helen and the Scream franchise.
Touching on her struggles, Klitschko said his former partner had also experienced the "darker sides" of Hollywood.
"She built an incredible career through immense talent, while also facing the darker sides of a very demanding industry," he said.
"Nothing will erase the times we shared or the place she had in our lives.
"To our daughter Kaya, I will always speak of her mother with respect and make sure she remembers the person she was.
"I extend my deepest condolences to Hayden's parents, her friends, and her fans, who are also grieving today. Young and talented people like Hayden should not leave this world so soon.
"I ask everyone to please respect our family's feelings and privacy during this incredibly difficult time. For now, this is all I wish to say."
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Panettiere spoke openly about her struggles with addiction through her 20s, as well as her experience of postpartum mental health following the birth of Kaya.
In a memoir published earlier this year, Panettiere spoke about the loss of her younger brother, Jansen, and her decision to give full custody of Kaya to Klitschko.
"The idea that anyone would think that I would just give away my child and be OK with it is heartbreaking and couldn't be further from the truth," she told podcaster Jay Shetty after the release of her memoir in May.
Panettiere said her daughter had lived with her father full-time from a young age as she battled addiction and poor mental health.
She said: "I was struggling with mental health and anxiety, and the postpartum and having to act my way through it and just feeling like I completely lost myself."
It's the biggest trial of its kind yet, with dozens of states seeking financial damages that could total as much as $1.4trn (£1.03tn).
Meta, which owns Facebook, Instagram, and WhatsApp, is accused of knowingly and deliberately designing features that get children addicted to its social media platforms.
It also claims that Meta routinely collects data on children under 13 without their parents' consent, in violation of federal law.
The company denies wrongdoing, and said in a statement: "We are proud of our record in protecting teens on our platforms and the amount of effort that we've put into developing protections over the years, even before these cases were ever filed."
While dozens of states filed the federal lawsuit three years ago, Tuesday's trial features four of those as plaintiffs - California, Colorado, Kentucky and New Jersey.
The other 25 states are expected to have trials later. Meta is also facing lawsuits from thousands of families over similar issues, as well as similar cases at the state level.
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Two trials found Meta liable for harm
It follows a landmark trial in New Mexico earlier this year, which found Meta knowingly harmed children's mental health and concealed what it knew about child sexual exploitation on its social media platforms.
The judge ordered the company to pay $567m (£421m) in damages - on top of the initial $375m (£280m) - and was also told to introduce new safety measures including a time limit of 90 hours per month for users under 18, AI chatbot restrictions, and mandatory warnings on the platforms.
It meant the penalty totals close to $1bn. Meta said it disagrees with the ruling and plans to appeal.
The company, along with Google, was also found liable by a court in Los Angeles in March for a woman's social media addiction - in what was hailed as a landmark ruling.
A jury found that Instagram and YouTube were responsible for harm caused to the woman - referred to in court as KGM or Kaley - who said she developed a number of mental health issues after using social media from a young age.
It marked the first time Meta CEO Mark Zuckerberg testified in court about child safety - which he will do again during this federal trial.
She was awarded $6m (£4.4m) in damages. Both companies disagree with the ruling and plan to appeal.
Sky News has learnt that Gordon Brothers is in talks with advisers about launching an auction process for Poundland, which employs about 12,000 people across Britain.
Industry sources said on Tuesday that Gordon Brothers had yet to make a final decision about a sale, but was likely to proceed with a process.
Advisers are expected to be appointed to oversee a prospective deal within days.
The prospect of another change of ownership will cast more uncertainty over Poundland's future, even as people close to the business insist that its financial performance has enjoyed an upturn.
Poundland now trades from roughly 600 shops, even after swingeing cuts implemented last year through a court-sanctioned restructuring plan.
Retail executives suggested that bidders were likely to include other turnaround funds, private equity firms or other industry players.
The chain's performance is understood to have stabilised in recent months, with Poundland expected to issue a trading update in the coming days.
In January, its managing director, Barry Williams said the business was "on the right track" months after coming close to collapse.
"While there's been significant progress as we re-focus and re-energise the business with lower prices and a sharper offer, we know we still have much to do," he said.
"Our focus on our costs has, without doubt, given us a platform for future growth, but no sustainable turnaround can be based on cost management alone.
"That's why our focus in 2026 will be on delivering the kind of ranges and price simplicity our customers want right across the store - in clothing, homewares as well as our core grocery aisles."
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Gordon Brothers acquired the discounter in July 2025 from Pepco Group, the Warsaw-listed retailer, for €1.
It has since appointed an experienced finance chief, Shaun Wills, who held the same role at fashion retailer Superdry.
Poundland serves millions of customers each year, and immediately prior to its restructuring employed more than 14,000 people.
Responding to an enquiry from Sky News on Tuesday morning, a Poundland spokesman said: "We've made very significant progress over the past year with a recovery plan that's created simpler, better value for customers centred around thousands of items back at our iconic £1 price point."
He declined to comment on the talks with advisers or the possibility of a new sale process.
Gordon Brothers, which also owns the LK Bennett and Radley fashion brands, did not respond to a request for comment.
It was unclear on Tuesday why Poundland's new owner was keen on such a swift exit from its investment if the business had begun to improve its performance.
The British high street remains caught in the crossfire of shaky consumer confidence and rising cost burdens, the latter of which has been exacerbated by government tax hikes.
Last week, Harvey Nichols, the department store chain, became the latest troubled retailer to be snapped up by billionaire Mike Ashley's Frasers Group when it underwent a pre-pack administration.
The UK Health Security Agency (UKHSA) said the salmonella outbreak "may be linked to eggs imported" from outside Britain.
From 11 August last year to the start of this month, the agency added that 207 cases have been confirmed - 199 in England, six in Scotland, one in Wales and one in Northern Ireland.
More than a third of people affected in the outbreak were admitted to hospital, while two developed potentially life-threatening bloodstream infections, the UKHSA said.
Those affected include babies and patients as old as 90.
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Hannah Charles, lead epidemiologist for gastrointestinal infections at UKHSA, added that it is working with the Food Standards Agency and other public health agencies to investigate the outbreak.
Earlier this year, the UKHSA said that salmonella cases were at a decade high in England, increasingly slightly from 10,389 in 2024 to 10,406 in 2025.
It noted in May that despite the rise, the figures "remain broadly comparable" to the year prior.
According to the NHS, salmonella symptoms generally include stomach cramps, diarrhoea, vomiting or fever.
Lee Ellis, 55, has been charged with manslaughter over the death of a man who was bitten by a German shepherd on a footpath in Wakefield on Saturday, West Yorkshire Police said.
He has also been charged with being in charge of a dog dangerously out of control, causing injury resulting in death.
Officers said he has been remanded in custody and is due to appear at Bradford Magistrates' Court on Tuesday.
It comes after officers were called to reports of an altercation on the old train line footpath off Blacker Lane, in the Calder Grove area of the town.
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The force said a 55-year-old man was bitten by a dog during the alleged altercation and later died in hospital.
A German shepherd seized by police as part of their investigation continues to be held in kennels.