Following victory, Rivlin declares: 'I am a man of the nation - long live the State of Israel!'
The bill, initiated by Finance Minister Yair Lapid, recognizes survivors who immigrated after 1953 and those persecuted by Nazis but not imprisoned in camps.
Reuven Rivlin and Meir Sheetrit awaiting the result of the vote to become 10th Israeli president. Result expected soon.
In shadow of Ben-Eliezer's graft probe, lawmakers will choose between five candidates, with no clear favorite.
Police, Tax Authority investigating allegations the Labor MK and former minister, who dropped out of the presidential race, didn't declare the cash held in a safe in a Jerusalem bank.
Decision to allow free vote follows the withdrawal from the contest of Labor candidate Benjamin Ben-Eliezer.
Many MKs wanted the election to replace President Shimon Peres delayed after MK Benjamin Ben-Eliezer dropped out amid scandal.
The bill, a copy of a similar law that was passed in the U.S. state of Oregon, would allow terminal patients to be prescribed an overdose of a lethal drug.
The cabinet had been meant to vote on the bill last week, but Netanyahu stripped it from the agenda due to legal issues in the wording.
Benjamin Ben-Eliezer's withdrawal Saturday from the presidential elections has sent MKs scrambling to find a new candidate.