The 10.5 tonnes of mail had been held in Jordan since 2010 because Israel would not permit direct transfer to the Palestinian Authority in the West Bank.
A rise in cross-border rockets and air strikes in recent weeks has prompted the United Nations and Egypt to try to broker a truce to prevent another all-out conflict.
Gaza, under years of grinding Israeli and Egyptian sanctions aimed at isolating Hamas, has seen a surge in tensions since Palestinians launched weekly border protests on March 30.
An Israeli drone attacked a Palestinian militant base in the northern Gaza Strip on Sunday, moderately injuring two people, security officials in the Hamas-ruled territory said.
Nabil Abu Rudeineh will serve as deputy prime minister and information minister, the government said.
The captain of a Norwegian boat carrying pro-Palestinian activists en route to Gaza has accused Israeli authorities of violating the law by boarding the vessel in international waters ...
Following the United States' decision to reduce UN funding for Palestinians, the United Nations Relief and Works Agency for Palestine Refugees (UNRWA) has cut its workforce in the Gaza Strip.
The military wing of Gaza's rulers Hamas on Thursday vowed revenge after Israeli strikes killed three militants in the latest flare-up of violence.
Israeli authorities say hundreds of fires have been started by firebombs since April.