Wanderers have been without a full-time boss since Neil Lennon left in March.
It had been thought that former Bristol City head coach Steve Cotterill and ex-Sheffield United manager Nigel Adkins were the frontrunners for the job.
But the League One club have instead turned to Parkinson, 48, who took charge of City in 2011 and helped them earn promotion from League Two in 2013.
The former Colchester, Charlton and Hull boss also oversaw the Bantams' run to the League Cup final in 2013, and led them to the quarter-finals of the FA Cup in 2015.
However, he was unable to guide Bradford to a further promotion in 2015-16, as a fifth-placed league finish was followed by defeat in the play-off semi-finals by Millwall.
Bolton suffered relegation from the Championship last term, having dealt with serious financial troubles off the pitch.
Wanderers appointed academy boss Jimmy Phillips as their interim manager following Lennon's departure, but he won only one of his nine games in charge.