The invitation was delivered to Israeli premier Sharon by Egyptian intelligence services chief Omar Suleiman in a meeting in Jerusalem.
"In light of progress in the security talks with the Palestinians, Egyptian President Mubarak has invited Prime Minister Sharon and Palestinian Authority chairman Mahmud Abbas to meet next Tuesday at Sharm el-Sheikh," a statement from the prime minister's office said.
"Prime Minister Sharon has accepted the invitation," the statement added.
At the end of a trip to Turkey, Abbas also confirmed he would be going to Egypt and expressed hope that the summit would yield positive results.
"We are hopeful," Abbas said. "We will go to the meeting with hope." The summit had been arranged due to the "critical stage the peace process is going through" and to "achieve concrete progress on the Palestinian track," said state media in Cairo.
After coming to power in February 2001, Sharon boycotted Abbas's late predecessor, Yasser Arafat, declaring him an obstacle to peace and kept him under virtual house arrest in the West Bank for nearly three years.
However, Arafat's death in November and Abbas's election on January 9 have prompted a renewed push for peace after more than four years of violence, which has claimed some 4,700 lives.
Both Abbas and Sharon have said they detect an "historic opportunity" to make progress in the peace process.
The two men met on a number of occasions in the summer of 2003 during Abbas's brief spell as prime minister, including at the launch of the roadmap peace plan.
The blueprint, which aims for the creation of a Palestinian state alongside a secure Israel, has made next to no progress although both Sharon and Abbas have emphasised that they remain committed to the plan.
Sharon, however, has been impressed by Abbas's recent efforts to halt the violence, including the deployment of thousands of troops throughout the Gaza Strip with orders to prevent anti-Israeli attacks.
Abbas has also managed to persuade armed groups to observe a temporary "cooling down" period.
The Palestinian president is trying to translate the temporary truce into a formal cease-fire but wants Israel to reciprocate by ending its military activities in the occupied territories and starting to release prisoners.
The ceasefire and prisoners issue are expected to top the agenda, according to Palestinian prime minister Ahmed Qorei.
"We are making very significant efforts to secure a cease-fire at the same time between us and the Israelis," he told reporters.
"We will respect whatever we are obliged to do in any agreement and we hope that this summit will be the beginning of the implementation of the roadmap."
Qorei said the Palestinians would like new US Secretary of State Condoleezza Rice to attend the summit. Rice is scheduled to be in Israel and the West Bank a day before the summit for talks with Abbas and, likely, Sharon on the evolving peace process but there was no indication from Washington that she would go to Egypt.