It was a key pledge President Maithripala Sirisena had made in the run-up to his January election win.
The bill needed two-thirds of the votes in the 225-member Parliament and 212 lawmakers voted in its favor with only one voting against. One lawmaker abstained and 10 others were absent.
The speaker does not usually vote.
The new law strips the office of immunity from lawsuits, brings back a two-term limit for president and transfers powers to appoint judges, police and bureaucrats to independent commissions.
Also, a president will not be able to dissolve Parliament at his or her will.
Former president Mahinda Rajapaksa who narrowly lost to Sirisena had concentrated more powers on the presidency abolishing a two-term limit and taking over powers to appoint all top officials.
Sirisena led a revolt in the party challenging Rajapaksa in the election and pledged that he would overhaul a system widely criticized as autocratic.
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