Browett will take up the position of senior vice-president of retail in April, reporting to Apple CEO Tim Cook.
Dixons has reacted by appointing a new group chief executive and a new chief executive for UK and Ireland, promoting from within for both positions.
Sebastian James, currrently group operations director, will take the former role and Katie Bickerstaffe, who has had responsibility for the launch of help service Knowhow, the store portfolio strategy, marketing, ecommerce, customer relationship management and human resources, will take the latter role.
There will be a handover period until Browett leaves the company on 20 April, but they will step up to the group board on 20 February and he will step down on the same date.
The news comes after Apple reported it had doubled profits in the final quarter of 2011, leading to speculation over what it would do with the $100bn (£63.5bn) cash pile its booming profit has created.
Cook said: "Our retail stores are all about customer service and John shares that commitment like no one else we've met."
Browett focused heavily on revamping the customer service at Dixons Retail, owner of Currys and PC World, after becoming chief executive in 2007.
In November, the retailer launched a multimillion-pound campaign spearheaded by a TV ad showing 'Star Wars' Darth Vader testing the knowledge of its staff in an attempt to change perceptions of its customer service.
Browett laid out three core tenets – "value, range and service" – after taking over the company.
Dixons offers staff bonuses only if their branch customer-satisfaction scores, calculated through exit surveys and mystery-shopper visits, reach a certain standard.
Prior to joining Dixons Retail, Browett was chief executive at Tesco.com and before that, he advised retail and consumer goods clients at Boston Consulting Group.
Follow Matthew Chapman at @mattchapmanUK