The versatile 27-year-old spent last season on loan at Torino, where he made 16 appearances in all competitions for the Granata before returning to the Rossoneri during the January transfer window.
“The Club wishes him all the best for the rest of the season.”
Laxalt will look to help the Scottish giants make history as they look to win ten-in-a-row.
“I’m extremely happy to have signed for a club that is very well known around the world,” he told the Celtic website.
“It is a club with a lot of tradition and I can’t wait to get out on the football pitch.
“I know there’s no game this weekend but I’m going to start training and I can’t wait to meet my new team-mates.
“And for me, when we’re standing in the tunnel and then out on the field, that’s when we start building up memories and building as a team.”