The oft-contested rebuild will see the museum in Old Rīga renovated by October 1, 2018 - in time for Latvia's founding centenary.
Furthermore, a memorial commemorating the victims of the Soviet occupation will be built on the Strēlnieku square and a white, rectangular annex will be added to the black monolith structure.
The extension, dubbed The House of the Future, would juxtapose Latvia's upcoming prosperity with the occupation under the Soviet Union and Nazi Germany.
The amendments were necessary so that the project would be carried out speedily and the annex could be built by Latvia's founding centenary, said Raivis Dzintars (National Alliance), chairman of a parliament committee responsible for drafting the law.
A year ago the museum annex plan was mostly a point of contention between architects.
The debates have taken on a political tinge, however, with the Rīga Municipal Construction Board rejecting the annex project and some seeing it as a political move by Harmony, which heads the Rīga City Council.
However now control over the reconstruction has been handed to the Ministry for Environment and Regional Development.
"The state fully overtakes granting the construction permit for both the Occupation Museum project and the memorial to the victims of the communist regime," said Saeima MP Ritvars Jansons.
The Museum of the Occupation of Latvia was built in 1971 to commemorate Lenin's 100th birthday. Following the collapse of the USSR, the building became a museum dedicated to Latvia's occupation by Soviet Russia and Nazi Germany.
The museum is funded mostly from private pockets - about one fourth of its funding comes from the state, while the rest is received in donations.
State investment for the rebuild is expected to be around €7.4m, and the museum has received about €1.5m in donations for the project.