The prime minister's office announced the death of the president on its official website and conveyed condolences early Wednesday.
“Today with deep sorrow we bid farewell to our beloved father, the ninth president of Israel,” his son Chemi said, according to various media reports.
“Our father’s legacy has always been to look to tomorrow. We were privileged to be part of his private family, but today we sense that the entire nation of Israel and the global community share this great loss. We share this pain together," he told reporters.
In a separate joint statement, U.S. presidential candidate Hillary Clinton and her husband Bill said they "lost a true and treasured friend".
Bill Clinton, who as president from 1993 to 2001 took part in the Oslo Accords process, tweeted a photo of himself with the deceased Israeli leader.
"I will miss Shimon Peres, my brilliant and eloquent friend. His life was a blessing to all who strive for peace," Clinton wrote.
A White House statement described Peres as "the essence of Israel itself".
"As Americans, we are in his debt because, having worked with every U.S. president since John F. Kennedy, no one did more over so many years as Shimon Peres to build the alliance between our two countries -- an unbreakable alliance that today is closer and stronger than it has ever been," the statement said.
Peres was Israeli president from 2007 to 2014 and a two-time prime minister.
He received the 1994 Nobel Peace Prize along with Yitzhak Rabin and Yasser Arafat for the peace talks he took part in as foreign minister, which resulted in the Oslo Accords.