The "Mission: Impossible" star was working with Tucci's future sister-in-law Emily Blunt on sci-fi action film "Edge of Tomorrow", when she explained she was heading out to a party and he asked if he could join her.
Tucci was thrilled to have the movie star as a guest, explaining Tom was great fun, and he was stunned when he received his wedding gift from his new pal.
"He noticed that both (wife) Felicity and I like to exercise and Tom is obviously the fittest man on earth, so he sent us this machine that athletes use," he tells Access Live. "It's like a cryogenic machine that freezes your muscles or something. It's this huge thing."
Tucci reveals Tom also sent the couple a joke gift after learning the newlyweds loved to cook - a spatula.