Montreal used targeted allocation money to secure the 28-year-old attacking midfielder, who has signed a three-year contract with the club.
Silva has earned four caps for Uruguay, most recently in June friendlies against Ireland and Italy.
"Alejandro is an attacking player who will bring his experience to the team and increase our options in the last third," Impact coach Remi Garde said in a news release. "His passing qualities and his speed will contribute in improving our play. His high work rate also makes him an option as a midfielder."
Silva played for Uruguayan side Fenix and Paraguayan club Olimpia before joining Lanus in 2014. He recorded 10 goals and eight assists in 58 games for Lanus during a stint that also included loans to Uruguayan side Penarol and back to Olimpia.
The winger has extensive experience in the Copa Libertadores, netting five goals and 11 assists over 37 games in the competition.
"Alejandro is a right-sided attacking player with a lot of experience playing in South America," Montreal technical director Adam Braz said.
"He will add a different dimension to the attack and will help improve the overall quality and depth of the team. His versatility on the field is very positive in that he can also play as a central midfielder."
The Impact are 1-2-0 to start the MLS campaign, having earned their first win under Garde with a 1-0 victory over Toronto FC on Saturday.
And Braz has indicated the club will be busy adding reinforcements in the coming weeks before the league's transfer window closes May 1.
"We are in discussions with other clubs regarding specific players that Remi has identified," Braz said. "We are hopeful that we can conclude certain moves in the not so distant future."