A spokesman for parliament said on Tuesday the law scraps a 75-year age cap for presidential candidates that was currently in place.
Museveni, 73, has ruled Uganda for 31 years and could now stand again in the next election, due in 2021, despite increased public anger over corruption, human rights violations and poor social services.
Parliament, controlled by Museveni's ruling National Resistance Movement (NRM), approved the constitutional amendment on December 22 amid heavy security deployments across the capital Kampala and outside parliament.
"It has been signed into law," spokesman Chris Obore said, adding that the president had done so on December 27.
Museveni's move quickly drew criticism from his political opponents, religious leaders, human rights activists and even some members of the ruling party.
Protests in September by opposition activists against the proposed amendment were quickly put down with detentions, teargas and beatings. At least two people were killed.
Some legislators opposed to the law tried unsuccessfully at various stages to filibuster it and some were suspended from proceedings. During the final debate on the amendment last month, some lawmakers scuffled with police.
Museveni is the latest of a growing list of African leaders who have either changed the law or used other tactics to thwart opponents and hold onto power long after their tenure has ended.
In Burundi, Democratic Republic of Congo and South Sudan, such moves have provoked instability.
Last month's vote by parliament was the second time the Ugandan legislature has amended the constitution to allow Museveni to stay in power. In 2005 they voted to remove a limit of two five-year terms, which had blocked him from standing again.
Despite the growing cries of autocracy against Museveni, Washington has backed him as a strongman who has turned Uganda into a bulwark of stability in Africa’s troubled Great Lakes region.
The landlocked East African country is eyeing commencement of crude production in 2020 and the construction of a pipeline to export it via neighbouring Tanzania is underway.
