The pair penned one-year deals at the Northern Commercials Stadium this week and will now join up with Stuart McCall's first team squad from next season.
Peters, 18, is a central midfielder, while Laird, who turns 18 later this month, plays mainly in central defence.
The duo have featured heavily for City's reserves in recent weeks, helping them secure four wins from the last five fixtures of their Central League campaign.
They have both come through the youth ranks at Valley Parade after originally joining the club at academy level.
Laird (pictured left) and Peters (pictured right) become the second and third of City's second year scholars this season to be awarded pro deals after Ellis Hudson signed a two-year contract last September.
Speaking about his move up into the professional ranks, Laird said: "This is something I've been working towards since I joined the academy as an under-13.
"I know what is expected of me and what I need to improve on but I really can't wait to get started next season.
"Playing in the reserve games (this season) has definitely been key to my development. I know it is a step up, physically it is different to playing youth team football. It is quicker and more intense.
"I've trained with the first team at times this season and I can't wait to now be training with them and learning from them every day.
"That can only help improve me as a player."
Peters added: "This is a big step up for me and I'm delighted to have been given this opportunity.
"I can't wait to be training among the first team players, I'm sure that will drive me on to want to get my game to their level.
"Danny (Devine) actually went to the same school as me and I've obviously played with him in the reserves and youth team.
"Seeing him come through and get appearances for the first team is a real positive. It is an inspiration to someone like me as well.
"It shows that if you aim for it and believe in yourself, you can achieve it.
"I just want to start pre-season as strong as I can and give it all I've got. Being a Bradford lad, it would mean everything to me to be able to play at Valley Parade for the first team."