Both main political parties, including that of President Robert Mugabe, had called for approval of the draft document, Voice of America reported Tuesday.
Mugabe, 89, has been in power since 1980 and will be allowed to seek another term in July's elections.
The new charter sets a limit of two five-years terms for the president. It also increases rights for women and bans the death penalty for women, the young and elderly.
More than 3 million Zimbabweans voted for the constitution, while 179,000 voted against.
A power-sharing agreement between Mugabe and Morgan Tsvangirai, now the prime minister, reached in 2008 required the drafting of a new constitution.
Charlize Theron not engaged to Sean Penn 'yet'
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards