Edgson, 20, already has Championship experience having spent the second half of last season with Rotherham Titans.
He also featured for National One side Blackheath and follows in the footsteps of Wasps colleagues Piers O’Conor and Alex Lundberg who joined the Blues from Wasps last season.
Wasps’ Senior Academy Manager Matt Davies said: “This is a great opportunity for George to test himself at a high level on a consistent basis.
"Bedford is a really well set up club and we’re confident that it is going to be a good environment for him to continue his development next season.
"We’re hoping it can have the same positive effect on his development as it has for Alex Lundberg and Piers O'Conor over the past 12 months.”
Blues’ Director of Rugby Mike Rayer said: “George is an impressive and eager hooker who is destined for big things and we are delighted to welcome him to Goldington Road."
Edgson said: “I am delighted to be joining Bedford next season. I really enjoyed my time playing with Rotherham Titans in the Championship last season and I can’t wait to get started with the Blues.”