75 of the 80 senators voted yes. The amendments, which have previously been hammered through the lower house, abolish direct presidential elections in the future - the president will instead be appointed by parliament - and extend the terms of office of the president and parliamentarians from five to seven years.
What remains is Mnangagwa's signature.
Critics have described the proposal as a "constitutional coup" feared to consolidate the ruling Zanu-PF party's grip on power.
Mnangagwa has ruled the country since 2017, when the military forced the authoritarian Robert Mugabe out after 37 years in power.
