The 25-year-old became the first British bantamweight to win Olympic gold for 104 years at London 2012, defeating Ireland's John Joe Nevin 14-11 in the final at the ExCeL.
Campbell, who joined the GB Boxing squad in 2007, enjoyed a highly successful amateur career, becoming the first Englishman for 53 years to win the European Championship in 2008.
He returned from surgery on his hand in 2009 to win silver at the 2011 World Championships but has left GB Boxing's World Class Performance Programme to turn professional.
Campbell has joined Eddie Hearn's Matchroom Sport and McCracken, who oversaw five British boxing medals at London 2012, is hoping for the best for him in the future.
He said: "Luke has been a great servant to the World Class Performance Programme for a number of years and an excellent role-model to other members of the squad in both his medal-winning performances and the way he conducts himself inside and outside of the gym.
"It is a disappointment for us that Luke has decided his future lies away from the GB Boxing squad but he departs with our best regards and we wish him every success in his future career.
"As we enter the Rio cycle, the majority of the boxers that competed in London remain part of our squad and we have some excellent talents coming through so the programme has a strong nucleus to work with and a good opportunity to add to the success we have enjoyed in recent years."
- Sports & Recreation