The Tigers outlined the 25-year-old as their main focus on day one of the Gillette AFL Player Exchange Period. He will provide support for No.1 ruckman Ivan Maric and allow Tyrone Vickery to spend more time in attack.
They've given up their second-round selection in next month's NAB AFL Draft, which is No.28 but likely to change as a result of compensation picks awarded for free agency.
"We identified Shaun Hampson as a player who will complement our existing ruck/key forward structure," said Richmond's list manager Blair Hartley.
"At 25 years of age we feel that Shaun's best football is ahead of him. Players over 200cm with Shaun's athletic qualities are hard to find.
"Over the past few years we have focused on recruiting players of great character and Shaun also fits this mould."
Despite Hampson's limited game time this season due to a knee injury and appendicitis, he was ranked sixth in contested marks per game.
The 63-game player was seeking consistent opportunities after slipping behind Carlton's Robbie Warnock.
"Shaun has been a much-liked and valued member of our team, who has a terrific work ethic," Carlton football manager Andrew McKay said.
"Although he hasn't played in many senior games this season, he has continued to make a significant contribution to the club behind the scenes.
"However, in the interests of both parties, there is a greater opportunity for Shaun at Richmond and it allows us another pick in the draft.
"We thank Shaun for his contribution to Carlton and wish him all the very best for the future."
Earlier on Monday, Richmond football manager Dan Richardson said Hampson was Richmond's "main focus" and dismissed reports linking the Tigers with delisted Geelong veteran Paul Chapman.
"I don't know where that comes from, actually. We haven't really had any discussion at all about Chappy," Richardson said.
"So best of luck to him, but not for us at this stage."
Richardson said Chapman, 32, was not a good fit for Richmond's young list.