They told of their "unspeakable grief" as the final body from the sunken Bayesian yacht, believed to be that of 18-year-old Hannah, was recovered on Friday.
"Their thoughts are with everyone affected by the tragedy," a statement on the family's behalf said. "They would like to sincerely thank the Italian coastguard, emergency services and all those who helped in the rescue."
Italian officials are investigating the circumstances around Monday's sinking, which also claimed the lives of five others on the boat.
Family and friends paid tribute to Mr Lynch, who helped pioneer a form of artificial intelligence, and his daughter, who had just won a place at the University of Oxford.
"Mike was the most brilliant mind and caring person I have ever known," a close friend, Andrew Kanter, said. "His passion for life, knowledge and all those around him was instantly inspiring to everyone he met, and he will be sorely missed."
"She is my little angel, my star," she added.
Gracie Lea, a classmate of Hannah, recalled her as "easy to love: sincere, dedicated, fiercely intelligent and genuinely kind. I’ll always remember her smiling".
She had recently finished her A-levels and had been offered a place to study English at Oxford, according to the Times.
"We are all incredibly shocked by the news," a spokesperson for her school, Latymer Upper, west London, said.
Among those who lost their lives in the disaster were Morgan Stanley International chairman Jonathan Bloomer and his wife Judy, a charity trustee.
In a statement the Bloomer family described the couple as "incredible people and an inspiration to many".
Clifford Chance lawyer Chris Morvillo, his wife, jeweller Neda Morvillo, and the boat's chef Recaldo Thomas also died in the disaster.
The gathering on the Lynch's yacht came after the end of a long-running legal battle over the sale of Mr Lynch's company Autonomy.
He was acquitted of multiple fraud charges in the US in June, over which he had been facing two decades in jail.
PA Media Group of fire service dive team in uniform next to a rescue boat, with emergency tents in the backgroundPA Media
The final body was recovered from the wreckage of the Bayesian on Friday
Italian authorities are still investigating the circumstances around Monday's incident.
In cases like this one, it is common for officials to embark on a broad investigation - known as a 'crime hypothesis' - that considers a series of possible criminal charges.
Approached by BBC News, the Italian police confirmed an investigation was ongoing but no charges have yet been brought.
The yacht's captain, James Cutfield, his eight surviving crew members and passengers have been questioned by the Coast Guard on behalf of prosecutors.
In a statement, Italian firefighters said it had been "five days of long and delicate operations in the sea, at a depth of about 50 metres (around 164 feet)."
After reports emerged that the final body had been found, a coastguard vessel which had been at the site of the shipwreck for hours could be seen back in the port.
Graphic showing yacht on seabed
Meanwhile, a helicopter landed nearby as divers took off their orange suits on the quayside.
A decision on whether to raise the sunken yacht from the seabed is "not on the agenda" but will be in the future, a spokesperson from the Italian Coastguard has said.
The ship was "practically intact" on the seabed, according to divers on the search and rescue team
A seventh body is recovered from sunken superyacht off Sicily, believed to be Mike Lynch’s daughter
Italian rescuers on Friday brought ashore the last of seven bodies from a superyacht that sunk off the coast of Sicily, the Coast Guard said. It is believed to be that of the daughter of British tech magnate Mike Lynch, who also perished when the boat sank earlier this week.
Hannah Lynch, 18, was the last person unaccounted for aboard The Bayesian, a 56-meter (184-foot) British-flagged yacht that went down in a storm early Monday.
Mike Lynch’s body was recovered Thursday. He had been celebrating his recent acquittal on fraud charges with his family and the people who had defended him at trial in the United States. His wife, Angela Bacares, was among the 15 survivors.
“The Lynch family is devastated, in shock and is being comforted and supported by family and friends. Their thoughts are with everyone affected by the tragedy,” a spokesperson for the family said in a statement issued Friday.
Rescuers struggled for four days to find all the missing bodies, making only slow headway through the interior of the wreck lying on the seabed 50 meters (164 feet) below the surface.
Civil protection officials said they believe the ship was struck by a tornado over the water, known as a waterspout, and sank quickly.
The other five victims are Christopher Morvillo, one of Lynch’s U.S. lawyers, and his wife, Neda; Jonathan Bloomer, chairman of Morgan Stanley’s London-based investment banking subsidiary, and his wife, Judy; and Recaldo Thomas, the yacht’s chef.
Termini Imerese Public Prosecutor’s Office investigators said it will hold a news conference on Saturday to unveil the first findings of its criminal investigation, which was opened immediately after the tragedy despite no formal suspects having been publicly identified.
The main question investigators are focusing on is how a sailing vessel deemed “unsinkable” by its manufacturer, Italian shipyard Perini Navi, sank while a nearby sailboat remained largely unscathed.
The Italian coast guard said Thursday the body of British tech magnate Mike Lynch is among those recovered off the coast of Sicily from the wreckage of a superyacht whose builders had called unsinkable.
One woman remains missing. She has not been identified, but Hannah Lynch, Lynch’s 18-year-old daughter, is reportedly unaccounted for. The family had been celebrating his recent acquittal on fraud charges with the people who defended him at trial in the United States.
Five others were recovered by rescue crews following Monday’s tragedy.
The Bayesian, a 56-meter (184-foot) British-flagged yacht, went down in a storm early Monday as it was moored about a kilometer (half a mile) offshore. Civil protection officials said they believe the ship was struck by a tornado over the water, known as a waterspout, and sank quickly.