Final figures from the elections commission showed the constitution was backed by 63.8 per cent of voters, giving Islamists their third straight victory at the polls since Hosni Mubarak was toppled in a 2011 revolution.
The yes vote, on an official turnout of 32.9 per cent, paves the way for a parliamentary election in about two months' time.
This is the first constitution since Mubarak's ouster.
Mursi's leftist, liberal, secularist and Christian opponents had taken to the streets to protest, saying the new constitution would dangerously mix politics and religion, but the president insists it offers sufficient protection for minorities and is necessary to end two years of turmoil and political uncertainty that has wrecked the economy.
The result of the referendum, held on 15 December and 22 December, was a disappointment for the opposition which had put pressure on the authorities to recount the result to reflect what they have described as major vote violations.