Laird said that manager Rob Edwards sold the club to him and he wants to be a part of the team that is hoping to push for promotion from League Two.
"I'm delighted," he told the club's official website. "I've been here training since last Thursday and I've enjoyed it. The lads have all made me feel really welcome and I'm glad I've joined.
"The club is a massive club in this division and the manager really spoke to me about the way he wants to play football because it suits my game. You've got to aim high. We want to get Tranmere back into the league above and push on from there."
Laird started his career at Manchester City.