The Maryland House voted 94-39 for a constitutional amendment already approved by the Senate.
The General Assembly, which is controlled by Democrats, sent the implementation bill to Hogan in time to override a veto, if the governor rejects the measure, before lawmakers adjourn April 11.
It also would automatically expunge the conviction of anyone previously found guilty of simple possession of marijuana, if it was the only charge in the case.
Currently, 18 states, along with the District of Columbia, have fully legalized marijuana.