The 22-year-old spent the second-half of last season on loan with the Shrimpers.
After signing on the dotted line, Bedeau said: "I am buzzing to get it all sorted, I can't wait to get going now and have two full seasons instead of just half a season which I had when I was on loan.
"The move has been in the pipeline for a few weeks, once my agent told me that Morecambe were interested again, I was really excited to come back as I really enjoyed my time here first time around.
"The fans were unreal, they helped in keeping us up last season and now it is a case of building on that and making sure that we consolidate our place in League One again.
"I know a lot of the boys from last year which is always nice, the manager came in after I did last season and was really good with me, so it was a very easy decision for me to come back.
"It ended on a real high note for the Club last year, we did really well to stay up, the fans, the players and everyone at the Club all managed to pull in one direction, which is what it is all about.
"The job now is to push on and establishing the Club as a League One side, and I want to play a part in that."