The 20-year-old defender has signed for the Championship outfit for the entire 2021/2022 campaign.
Laird, who will wear the no.27 shirt with the Welsh outfit, worked under Martin when the latter was manager of MK Dons last term.
"I am buzzing, I cannot wait to get started and get out on the pitch," said Laird, per the club website.
"This is a big club, a very big club, and the type of club I want to play for. I played here once before at the stadium when I was 16 (for Manchester United Under-23s) and I really enjoyed it.
"It was exciting to watch the game against Sheffield United, the fans here are intense and I cannot wait to play in front of them.
"I just want to get out there and experience it.
"I also love working with Russell and I just know he can get the best out of me. The big thing about him is trust. When I came in from United, he told me exactly how it was straight away.
"I just learnt so much in that short amount of time, it was unbelievable so I knew if I worked with him again, I could continue to improve and develop.
"I love the style of play. I think it is the best way to play football, it is entertaining, and it is how you want to see your team play, getting those passes in. That's what I enjoy and that's why I am here."
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