"The decision to award Malala the prize is a worthy one," Peres, 91, said in a statement.
"She is a symbol to women and girls across the world and an example to all of us," he said, paying tribute to the youngest Peace Prize laureate.
"Malala, you defeated those who tried to silence you and your victory is a victory for peace. We are all proud of you."
The Nobel Peace Prize was awarded jointly Friday to 17-year-old Yousafzai, who survived being shot in the head by the Taliban, and to India's Kailash Satyarthi for their championing of children's rights.
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Malala heard the news while in class at her school in Birmingham, England, where she moved from Pakistan to receive life-saving treatment two years ago.
The Norwegian Nobel Committee said the duo had been chosen for their struggle against the repression of children and young people and "for the right of all children to education".
Malala, who had fought for years for the right of girls to education in her strictly Muslim home region, leapt to global fame after the Taliban tried to gun her down in October 2012.
Peres was awarded the 1994 Nobel Peace Prize as foreign minister jointly with prime minister Yitzhak Rabin and then Palestinian leader Yasser Arafat for Israel's 1993 Oslo Accords with the Palestine Liberation Organisation.