A senior Palestinian official said a first group of 450 Palestinian prisoners would be released next Tuesday, followed by Shalit's release on Wednesday.
The Israeli soldier would be taken first to Egypt, via the Rafah border crossing, and then flown to Israel, the official said. It was not clear if Shalit would be flown home from Cairo or elsewhere in Egypt.
Israeli media too reported that Shalit was expected home on either the Tuesday or Wednesday.
That assessment was backed by an announcement from the Israeli justice department, which said a list of Palestinian prisoners to be released in exchange for Shalit would be published on Sunday, and that the Israeli public would have 48 hours to raise any legal challenges.
Officials from Israel and the Hamas movement have said they expect the first stage of the exchange to begin "within days."
Under the Egypt-mediated deal, a group of at least 450 Palestinian prisoners will be released along with Shalit in the first phase of the deal, followed by the release of another 550 Palestinians within two months.
It was still unclear when an additional group of 27 Palestinian female prisoners to be freed under the deal would be released.
Israeli news site Ynet reported that Shalit would be transferred from Gaza to Egypt via the Rafah border crossing in the middle of next week and then flown to Israel. Reports in the Egyptian media that Shalit has already been freed and is in Egypt remain unconfirmed and are likely false.
The news site said Shalit's parents would meet him at a military base, where he was likely to also be greeted by Prime Minister Benjamin Netanyahu.
He is expected to receive immediate medical treatment and will be accompanied by military psychologists throughout, the website reported.
Shalit has been held since his June 25, 2006 capture in a cross-border raid by militants from three Gaza groups - Hamas, the Popular Resistance Committees and the Army of Islam.
Negotiations to secure his release in exchange for hundreds of Palestinians held in Israeli prisons have stalled multiple times over the names of those to be freed and where they would go.
The deal announced Tuesday night will see some detainees from the West Bank exiled to Gaza or overseas, and it excludes some high-profile Palestinian prisoners, including Fatah leader Marwan Barghuti and Ahmed Saadat, the secretary general of the leftist Popular Front for the Liberation of Palestine.