The 21-year-old helped Bournemouth achieve promotion to the Premier League last season, after joining on a temporary move in January, following the end of his successful period at Swansea City.
Laird, who has been with United since the age of 10, spent pre-season with the first-team, featuring twice on the tour of Thailand and Australia, and also in the game against Rayo Vallecano at Old Trafford.
The full-back will now join up with new QPR boss Michael Beale. Laird could make his debut as early as Tuesday night, in the Championship game against Blackpool, subject to confirmation of registration by the FA and EFL.