Approved overwhelmingly in a referendum in March this year, the constitution clips the powers of the president, limits presidential tenures to two five-year terms and does away with the post of prime minister.
However, it does not apply retroactively so the 89-year-old Mugabe could technically extend his three decades in office by another 10 years.
"This day is an historic day, it's about the future," Eric Matinenga, the Constitutional Affairs Minister said at the signing ceremony.
"I can assure you that this document which is before us is a good document."
A new constitution is one of the pre-conditions for elections to pick a successor to the shaky compromise government Mugabe formed four years ago with Tsvangirai.