The Shin Bet said in a statement Sunday that Sharawneh could leave Gaza after the 10-year period "if he hasn't returned to terror activity."
Sharawneh was among four Palestinian prisoners who have been on a long-term hunger strike.
Another, Samer Issawi, has been on a hunger strike for over seven months. He began refusing food in August, when he was detained. He has taken nutrients in a hospital drip from time to time to stay alive, although his health condition is considered grave.
Issawi was sentenced to 26 years in prison for his involvement in a series of shooting attacks targeting Israeli police cars and students at the Hebrew University in Jerusalem.
Issawi was also freed as part of the 2011 prisoner exchange and was re-arrested for violating his release conditions.
The two other hunger strikers, Tarek Qaadan and Jafar Ezzeldeen, are in administrative detention, a system where prisoners can be held indefinitely without being charged, in three-month renewable periods. They began refusing food when they were detained over four months ago.
Israeli security officials suspect the two men are members of the violent Palestinian group Islamic Jihad and were overseeing militant activity, but neither has been charged.
About 4,000 Palestinians are in Israeli prisons for crimes ranging from throwing rocks at soldiers to deadly militant attacks. Palestinians see them as fighting for their national liberation, while Israelis widely regard them as terrorists.
West Bank protests demanding their release have repeatedly turned violent in recent weeks.
Associated Press writer Diaa Hadid in Gaza City contributed to this report.