The left winger has signed a two-year deal on the day that Alan O'Brien's contract was cancelled by mutual consent.
Galashiels-born Galbraith, 19, signed for United on his 16th birthday and has represented Scotland at several age levels.
Galbraith told Hibs' website: "I'm delighted to be returning to Scotland and in particular to Hibernian.
"I really enjoyed my time at Manchester United but the time was right for me to seek a new challenge with first-team football my main aim.
"I know that will be a tough task in itself as there are a lot of quality players in my age group stepping up from the successful Hibernian Under-19 side, but I've never shied away from a challenge in my career."
Hibs boss John Hughes has made Galbraith his second signing following the capture of midfielder Patrick Cregg from Falkirk.
Hughes, who lost star player Steven Fletcher in a £3m move to Burnley on Tuesday, said: "Daniel arrives at Hibernian with a great attitude and the best of his career ahead of him.
"He was unlucky with injuries at Manchester United, but is very young with good energy about the park.
"He has his whole career ahead of him and has shown he can play a variety of positions on the left-hand side.
"I'm really looking forward to working with him as he will provide great competition for places and I'm sure we're going to get the best out of him."