The Australian front-rower had a year left on his Leeds deal, but his departure will open up a second space on Rhinos’ overseas quota.
Garbutt joined Rhinos from Melbourne Storm midway through the 2015 season and helped them win the Challenge Cup, against Hull KR, league leaders’ shield and Grand Final in his first 14 games for the club.
In total he scored nine tries in 72 appearances for Rhinos, but a succession of knee injuries limited him to just nine games this year.
The Yorkshire Evening Post revealed last month Garbutt was among a number of contracted players who would be allowed to leave if they they could agree a deal at another club.
The 29-year-old said: “The opportunity came up to leave Leeds, I had a chat with a few people and then met with Tim [Sheens, Hull KR’s coach] and he was really good.
“He was really straightforward with what he wanted and I think I’ll fit in really well.”
He added: “I would like to thank the Leeds Rhinos supporters who have always given me and my family great support during my time at the club.
“We have created some fantastic memories that will always live with me.”
Rhinos’ director of rugby Kevin Sinfield said: “We would like to wish Mitch all the best at Hull KR. He has been a popular member of our squad throughout his time here, he leaves with our thanks and best wishes for the future.”
Garbutt’s move reunites him with former Rhinos team-mate Danny McGuire who has confirmed 2019 will be his final season as a player.
Robins coach Sheens said: “Mitch brings a wealth of experience to our team and joins what is now an impressive and experienced front-row including Robbie Mulhern, Lee Jewitt, Mose Masoe and Nick Scruton.
“When a player of Mitch’s ability becomes available it’s important to move quickly to tie them down and we’re delighted we’ve been able to secure his services until 2021.”
Former Leeds coach Brian McDermott, who took training for the first time at Toronto Wolfpack yesterday, will retain Simon Finnigan and Kurt Haggerty as his assistants.