Burns, 28, is likely to replace Blake Green, who looks set to sign for Wigan for 2013.
The Australian worked with current Rovers coach Craig Sandercock at Manly, and saw his 2012 season cut short by a 12-match ban.
Burns said: “Myself and my family are very excited about heading over to Hull KR.
“I’ve been watching a lot of the games on TV and I see a young team which is not far off being a real force in the Super League.
“Opting to join Hull KR was an easy decision for me as I know that the people of Hull are very friendly and love their football.
“Craig was also a big reason why I decided to sign. He was an assistant coach when I started my NRL career at Manly and I always knew he would coach at the highest level.
“The conversations I’ve had with him about his plans for me and the club going forward made my decision easy and I can’t wait to pull on a Robins’ jersey for the first time.”
Burns has also played for Manly and North Queensland in the NRL, scoring 22 tries and 41 goals in more than 100 appearances.
He becomes the fourth new signing for Sandercock’s squad for next season, following on from the captures of Salford centre Sean Gleeson, North Queensland back-rower Cory Paterson and Newcastle prop Evarn Tuimavave.