Prime Minister Benjamin Netanyahu spoke with Sisi and "congratulated him on his victory in the election," the premier's office said.
A statement noted "the strategic importance of the ties between the states and of upholding the peace agreement, and wished the Egyptian people a future of stability, prosperity and peace."
Shimon Peres's office said the Israeli president told Sisi: "Israel is committed to maintain the peace treaty between Israel and Egypt and to strengthening the cooperation between our nations."
Peres too wished the Egyptian people "prosperity and success" and said he hoped Sisi would lead Egypt to "great achievements".
Sisi was declared Egypt's president-elect Tuesday following an election last week, nearly a year after he toppled Islamist president Mohamed Morsi.
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The former field marshal is to be sworn in on Sunday.
Egypt in 1979 became the first Arab country to sign a peace treaty with Israel, but ties have remained formally cold over Israel's policies towards the Palestinians.
Ties frayed further after president Hosni Mubarak's ouster in 2011, hitting a low point when protesters stormed the Israeli embassy in Cairo later that year.
Last month, Sisi implied he would not receive an Israeli premier in Egypt until a Palestinian state is established, with east Jerusalem its capital.
The Egyptian military is engaged in a counter insurgency campaign against Islamist militants in the Sinai Peninsula near Israel's border who have killed hundreds of security personal and also attacked Israel.
Israel has also voiced support for a crackdown by Egypt on smuggling tunnels linking Sinai with the Gaza Strip, controlled by the Islamist movement Hamas until this week's formation of a Palestinian unity government.