Barcelona will use the stadium between August 2023 and May 2024.
The Catalan giants are expected to move out from the legendary Camp Nou as renovation work would be carried out this year.
They will be able to play the 2022/23 season and the move next season would cost the club somewhere between €15m and €20m.
Olympic Stadium has a capacity of 60,713 and was previously home to local rivals Espanyol.
Laporta said in an official statement: “At FC Barcelona we have committed to adapting the Olympic facilities and ensuring the comfort of our members and fans on match day and we will modernise various services or auxiliary spaces such as the press room, changing rooms and an internal parking area.
“We estimate that the move to Montjuïc will cost Barça between 15 and 20 million euros. We are talking about an iconic stadium of the Barcelona Olympics, we are talking about an international reference for the city and at Barça, what we would like during the season that we are here is that it be the epicentre of Barcelona, shared with the great city that is Barcelona.
“All the members and subscribers who want to come to the stadium will do so through a democratic system and everyone can come by rotation, to ensure that as many Barcelona fans as possible can have access to the Olympic Stadium.”