One focus of Monday's talks will be the situation in the Gaza Strip, where Egypt helped broker a ceasefire after 11 days of conflict in May between Israel and Hamas, the Palestinian faction that controls the enclave, diplomatic and security sources said.
An uptick in cross-border violence since late August has tested the fragile truce. Over the past week, Palestinian militants have fired rockets into Israel for three nights in a row, drawing Israeli air strikes.
Bennett and Sisi were also expected to discuss regional issues, including Iran's influence in the Middle East and the crisis in Lebanon, diplomats said.
The trip appeared to give transport links between the two countries a boost.
The Taba crossing between Israel and Sinai, an entry point for Israeli tourists, would become fully operational from Monday as restrictions put in place during the coronavirus pandemic were lifted, Israel's transport ministry said.
From October, Egyptair would begin operating several flights a week between Cairo and Tel Aviv, sources at the Egyptian national carrier said.
Egypt became the first Arab country to sign a peace treaty with Israel in 1979 but relations have remained cool, restricted to security cooperation and limited economic links.
Egypt's brokering of the Gaza truce allowed it to reassert its diplomatic role in the region in the wake of deals by four Arab states to normalise ties with Israel last year.
The last official visit by an Israeli prime minister to Egypt was when Benjamin Netanyahu met former Egyptian president Hosni Mubarak in January 2011 in Sharm el-Sheikh, just before the uprising that toppled Mubarak.