The 20-year-old made six appearances for the Bulls and enjoyed a loan spell with Hunslet last season.
Lawford, who has represented Yorkshire at academy level, was offered an extended contract on significantly improved terms but turned it down to join Championship rivals Wakefield, the Bulls said in a statement.
Trinity have paid a compensation fee to land the Bradford academy product.
Lawford will join Jermaine McGillvary and Lachlan Walmsley among the fresh faces at Belle Vue next year.
Trinity boss Daryl Powell, who took over from Mark Applegarth following the club's relegation, expects the youngster to thrive in the set-up at Belle Vue.
"This is a quality signing for our future," said Powell.
"Myles is a young half-back with class written all over him. He will have a couple of outstanding mentors in Luke (Gale) and Mason (Lino) as he steps into full-time training for the first time.
"I’ve no doubt he will challenge those two for a place in the starting team next season.
"I look forward to helping him grow into the player we all know he will become."