Elias Zananieri, a spokesman for Palestinian security chief Mohammed Dahlan, said on Friday the cities are Jericho, Ramallah, Qalqilya and Tulkarem.
He said the Israelis have also promised to remove barricades at the entrances of the four towns, and increase the number of licenses given to Palestinian tradesmen and workers to enter Israel.
The agreement was reached during a two-hour meeting in Jerusalem between Dahlan and Israeli defence minister Shaul Mofaz.
The pair met late on Thursday evening in a bid to rescue a ceasefire declared by Palestinian resistance groups in late June.
No Israeli officials were available to confirm the planned withdrawals.
Israel has agreed to withdraw
Security officials from both sides are to hold a meeting on Sunday to discuss the details of the transfer of authority, Zananieri said.
However, a report on Israeli public radio said while Israel would transfer control of Jericho and Qalqilya next week, it would only hand over Ramallah and Tulkarem if the Palestinians met certain conditions.
These were an end to anti-Israeli attacks and demands that the Palestinians draw up a detailed plan on fighting “terror”.
Israel Army radio added Dahlan had committed himself to collecting weapons from Palestinian resistance groups and identifying their sources of funding.
Mofaz and Dahlan last met two weeks ago but the meeting ended in failure after Mofaz refused to pull troops out of the West Bank cities of Hebron and Ramallah.