Collyer, 18, is expected to become the first signing under interim manager Ralf Rangnick, who will take up a consultancy role at Old Trafford at the end of the season.
Born in 2004, the youngster leaves the south coast with huge pedigree, having captained England's Under-16 and Under-17 sides already.
According to transfer expert Fabrizio Romano, Collyer joins the Red Devils on a three-and-a-half-year deal, with his contract running until the summer of 2025.
Having impressed on trial at Carrington last month, he caught the eye of United scouts at Brighton in a friendly against Huddersfield Town.
A versatile player, the talented teenager can operate in both central midfield and centre-back.
United have signed several young players for their academy in recent years, including Charlie McNeill, Joe Hugill and Ethan Ennis, with Collyer now joining the trio.
Rangnick previously spoke about how United's transfer strategy was unclear earlier this season - calling on club chiefs to follow in the footsteps of their rivals.
"It's about having a clear transfer strategy and signing players who fit into that system. And that's what both clubs (City and Liverpool) have been doing in the last five or six years," Rangnick admitted.
"If I look at their transfer policy and their transfer success, they haven't had many players who people would say that maybe that wasn't the right signing. Both clubs have been pretty successful - and this is where Manchester United have to go again."