The pair appeared together in Steven Spielberg's 1989 sequel Indiana Jones and the Last Crusade, with Sir Sean playing Ford's father Henry Jones.
"He was my father... not in life... but in Indy III," said Harrison in an interview with Variety.
"God we had fun - if he's in heaven, I hope they have golf courses. Rest in peace, dear friend," he added.
Ford recalled the "pleasure" of taking Sir Sean "for a ride in the sidecar of a Russian motorcycle, bouncing along a bumpy, twisty mountain trail and getting to watch him squirm".
Ford's tribute to the James Bond actor follows those of many other Hollywood stars.
Robert De Niro, Kevin Costner, Sir Michael Caine, Daniel Craig, George Lazenby and Pierce Brosnan have all praised the late actor.
Brosnan, who himself played the role of 007, posted online that Sir Sean was "my greatest James Bond as a boy, and as a man who became James Bond himself".
The family of another late former Bond star, Sir Roger Moore, also tweeted to say that he too had "always maintained Sean was the best ever James Bond".
Sir Sean was best known for his portrayal of James Bond in seven films from 1962 to 1983. They included Dr No, From Russia with Love and Goldfinger.
He died in his sleep in the Bahamas, surrounded by his family.
His widow has since confirmed that her husband had been diagnosed with dementia.
"It was no life for him," Roquebrune told The Mail on Sunday.
"He had dementia and it took its toll on him. He got his final wish to slip away without any fuss."
She added the actor "was not able to express himself" in the period leading up to his death.
Over the course of his career, Sir Sean won an Oscar, two Baftas and three Golden Globes.