The 454-member parliament unanimously agreed to the president's request on Wednesday.
The decision was taken while about 200 opposition supporters protested outside the assembly against what they said were tactics to ensure either Mubarak or his son was elected.
The move enables Egypt to hold its first presidential election with more than one candidate since the military overthrew the monarchy in 1952.
The amendment, however, is said to impose restrictions that make it difficult for opposition parties to present a competitive candidate.
"The amendment is dubious and will serve the father and his son," chanted the protesters.
Working out the rules
The parliament's legislative committee will now work out the rules for nominating presidential candidates and supervising the election.
Egyptians have expressed
scepticism over the amendment
The work should be completed in two months, said Ahmad Abu Zaid, a member of the committee for the ruling National Democratic Party.
The committee's recommendations have to be approved by parliament and then go to a national referendum, which might be held by the end of May.
Until now Egypt has held presidential referendums in which people voted yes or no for a single candidate approved by parliament.