Peres had earlier taken a commanding lead in the first round of voting, prompting his two rivals to withdraw from the race - making him the sole candidate in the second round.
Peres, who has never won a national election outright in Israel but has served twice as prime minister, had taken 58 ballots in the first round, short of the 61 needed for victory.
Born in Poland, Peres immigrated before Israel achieved statehood and rose through Labour's ranks as an ally of David Ben-Gurion, the country's first prime minister.
As defence minister in the late 1950s Peres secured a secret deal with France to launch an Israeli nuclear programme.
Israel reportedly used the programme to produce atomic weapons, but Israel has never openly admitted this.
Peres served as prime minister from 1984 to 1986 and then again in 1995 after the assassination of Yitzhak Rabin, but never won an election for the position outright.
Peres won a Nobel prize alongside Rabin and Yasser Arafat, the late Palestinian president, for a 1993 interim peace deal.
It was Israel's first accord with the Palestinians that led to the establishment of limited Palestinian self-rule in Gaza and the occupied West Bank.
Peres would be sworn in next month when Katsav formally ends his seven-year term of office.
Katsav is on a leave of absence since legal authorities said in January they intend to charge him with raping an employee and sexually assaulting several other women who worked for him.
While the presidency does not entail any direct involvement in policymaking, Israeli presidents have traditionally spoken out on issues often influencing political decisions. The president also often holds talks with world leaders.