Brown, 46, has agreed a three-year contract with the Rams and he takes over from George Burley, who resigned early in June.
He worked alongside Bolton boss Sam Allardyce at Blackpool and has been his assistant at Wanderers since late 1999.
Brown was also linked with the Burnley job before Steve Cotterill was appointed last year.
Former Bolton defender Brown has played a key part in the club's recent success and last season he helped them qualify for Europe for the first time in their history.
But he has made no secret of his ambition to test his own managerial skills.
Derby and Bolton are thought to have already agreed a compensation package.
