Donny beat off interest from Ronnie Moore's Oldham side to sign the 24-year-old ex-Notts County striker, and the Irishman has signed a three-year deal at Belle Vue.
Heffernan told the club's official website: "I had a chat with the people at Bristol and told them I did not want to have another season sat on the bench and the manager agreed with me.
"When Doncaster approached Bristol I decided to come and see what they had to offer, so I met Dave Penney and liked what I saw and heard."
Chairman John Ryan was delighted with the club record swoop, and Donny's fourth arrival of the summer.
He explained: "This shows our commitment to bring in quality players who will help us go for it next season.
"I have broken the club record to bring in Paul who is a proven goal scorer at this level and with the fans support we will get other targets to join the club.
"It shows that we can attract players of his quality to Rovers"