The 33-year-old Hull fighter triumphed in the bantamweight division at the London Games before turning professional.
He won 20 of his professional fights and lost four.
Campbell said: “I guess there is no better time to announce my retirement from boxing. It has been one hell of a ride, a roller-coaster of highs and lows.
“I’ve achieved my dream, which was the Olympics, the gold medal. That was my dream. The professional side of boxing was just a bonus for me. I’ve got some memories for life.
“I’ve been on the road for 20 years and boxing for 22. For me, it’s time. I want to be with my family and dedicate myself to them.
“It’s not been an easy decision. Boxing is my identity. It’s who I have been for most of my life. Before making this decision there were many sleepless nights and going to bed crying and upset just coming to terms with it.
“Now, I can finally say I am content with that. I am happy and loving life.”
Campbell twice fought for the world lightweight title but was beaten in 2017 by Jorge Linares and Vasiliy Lomachenko two years later.
He added: “The past year in boxing though has been tough. An extremely long training camp away from family meant I was only able to spend a few days with my new-born child and also resulted in me having Christmas apart from them on the other side of the world.
“It’s in these moments that you realise what is truly important in life. I’ve lived my dreams and accomplished more than I ever imagined I would.
“In the same way that my dad was able to witness my greatest achievements, I want to be able to do that for my children and make sure I’m always there to see their biggest triumphs.”
Eddie Hearn says a long-awaited fight between Anthony Joshua and Tyson Fury could be possible in February, but only if Joshua looks after his business against Oleksandr Usyk.
Joshua was finally due to get in the ring for a blockbusting unification fight against Fury, but it was cancelled after a United States arbitrator ordered the latter to have a third bout against Deontay Wilder.
That left the WBA, IBF and WBO heavyweight champion to fight undisputed world cruiserweight champion Usyk at the end of September at the Tottenham Hotspur Stadium.
But Joshua-Fury is the fight that everyone wants to see and promoter Hearn thinks it could be possible in early 2022.
“I think I would probably say a February date or something like that, but after all the negotiations we are just focused on Oleksandr Usyk and we’ll go from there,” he said.
“I would like to think we have got a good deal in place for that, but I don’t really trust anything that comes from that side.
“But if we don’t beat Usyk, it’s irrelevant anyway so that’s the focus.”
Conor Benn’s WBA continental welterweight title defence with against Adrian Granados has been postponed after the British boxer tested positive for Covid-19.