The Lancastrian - whose six league appearances thus far term had come off the bench, including in Saturday's 2-1 loss at Crawley Town - has signed for County on a three-year deal for an undisclosed fee.
Crankshaw only joined the Bantams on deadline day at the end of the winter transfer window from Wigan Athletic, again for an undisclosed fee.
The 23-year-old, a former trainee at Preston and Morecambe, signed a two-and-a-half-year deal and had been contracted at Bradford until June 2023.
On his exit, Crankshaw said: "This is a bittersweet moment for me, but I have to do what I feel is right for my footballing career and development as a player.
"I would like to start off by saying a huge thanks to all Bradford City supporters who welcomed me with open arms through COVID and during the start of this season.
"Stockport County have offered me a platform to play and achieve my aims as a footballer, which I felt I could not turn down.
"I would like to thank everyone at Bradford City for the opportunity and wish the club the very best for the future."
Bantams boss Derek Adams said: “Ollie leaves with our best wishes, having received a substantial offer from Stockport which he felt he could not turn down.
"We would have liked to keep him at the club and seen him fight for his place in the side, but understand and respect his decision to leave.
"As always, we will never stand in the way of anyone who sees their future away from Valley Parade.
"I would like to take this opportunity to thank Ollie for his efforts at Bradford City."