After signing a one-year deal with City last summer, Dolan's current deal with the Bantams will now expire at the end of next month.
Speaking about Dolan's departure, Parkinson said: "I sat down with Matty this week and had a good chat with him.
"While he has become a valuable squad member, I feel it will be good for Matty to become a regular starter somewhere so that he can progress his own career.
"Matty has been a good part of our squad this season, a good person to have around the dressing room, and we wish him all the very best for the future."
After making eleven appearances for City while on loan from Middlesbrough during the 2013/2014 campaign, Dolan made his move to Valley Parade a permanent one exactly a year ago tomorrow (16 May).
Dolan featured eighteen times for City last season, mainly from the bench, although he did start the club's last fixture of the season at Crewe Alexandra earlier this month.
He also spent a brief loan spell back with former club Hartlepool United during the 2014/2015 season, although that deal was unfortunately cut short due to injury.