The Scottish actor died at the weekend in the Bahamas at the age of 90.
Ford and Sir Sean appeared alongside each other in 1989’s Indiana Jones And The Last Crusade.
In a statement, Ford said: “He was my father… not in life… but in Indy 3.
“You don’t know pleasure until someone pays you to take Sean Connery for a ride in the sidecar of a Russian motorcycle bouncing along a bumpy, twisty mountain trail and getting to watch him squirm.
“God we had fun – if he’s in heaven, I hope they have golf courses.
“Rest in peace, dear friend.”
Filmmaker George Lucas, who produced the Indiana Jones films and originally pitched the swashbuckling archaeologist as being a character concept “better than James Bond”, also paid tribute to Connery over the weekend saying: “He will always hold a special place in my heart as Indy’s dad.
“With an air of intelligent authority and sly sense of comedic mischief, only someone like Sean Connery could render Indiana Jones immediately into boyish regret or relief through a stern fatherly chiding or rejoiceful hug. I’m thankful for having had the good fortune to have known and worked with him.”
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 remembered the late actor.
Sir Sean was the first actor to play 007 on the big screen in Dr No in 1962.
This was followed by From Russia With Love, Goldfinger, Thunderball, You Only Live Twice and Diamonds Are Forever.
Over the course of his career, he also won an Oscar, two Baftas and three Golden Globes.