Since then, Hamas has accused Israel of trying to pressure the group into freeing the soldier.
Dweik, who Hamas have suggested could become a possible candidate for the presidency, was taken to a hospital in Israel several times to be treated for high blood pressure and diabetes during his imprisonment.
It remains unclear whether his health conditions contributed to the decision to release him. His lawyer, Fadi Kawasimi, said inmates' terms routinely are shortened by several months for good behaviour.
Hamas did not reveal whether Dweik would resume his duties as parliament speaker.
Al Jazeera's Jacky Rowland reported that Dweik declined to answer questions from reporters and said he would issue a statement from the Palestinian parliament in the West Bank city of Ramallah later in the day.
She also said that this is not a time of celebration for the Palestinians as dozens of Hamas parliamentary members still remain in Israeli jails.
"He will be very keen to remind people of the fact that although he is out, many of his fellow parliamentarians are still being held in Israeli jails, many of whom haven't been given a trial," she said.