The 30-year-old, who still has a year remaining on his contract at Rovers, will join the Minor Premiers next season in a deal understood to be close to matching the £100,000 Wigan Warriors paid KR for Blake Green, who Burns replaced two years ago.
Wigan were also reportedly keen on signing Burns with Green returning to the NRL, but it's Saints who have heavily invested to find a half-back partner for Luke Walsh.
The Mail understands Burns has signed a three-year contract at Langtree Park.
Burns' expected departure now leaves the Robins with a search on to find both a replacement stand-off and a hooker as Chris Chester plans for his first full season in charge of the Robins.
First-choice hooker Josh Hodgson, who won both player of the year awards this season, has signed a two-year contract with NRL side Canberra Raiders and his loss will now be amplified even more by Burns' departure.
With a quota place once again available, Rovers are starting their search in Australia, with CEO Mike Smith currently Down Under speaking to agents.
Rovers are eager to find an experienced replacement to partner Kris Keating, who had an average first season having been brought in to replace Michael Dobson at scrum-half.
While expecting Burns to go, the loss of his stand-off is a major blow for Chester's rebuilding plans as he puts together a side which he hopes will compete and challenge for a place in the top eight of the newly restructured Super League.
Burns was the linchpin for Rovers this season with the majority of the plays involving him rather than his half-back partner Keating.
When asked about Burns' future at the weekend, Chester reiterated the star was contracted to Rovers but he wouldn't stand in the player's way if the deal was right for the club.
A fee of £100,000 represents good business for KR, but they need to work fast if they are to have a stand-off in place for the start of pre-season training.
Burns is the third half-back to leave the Robins in the last two years.
After Green joined Wigan and was replaced by Burns, Dobson returned to Australia to play for Newcastle Knights.
Rovers will take pride in the fact they can develop players to a high standard, but will be disappointed they've once again been unable to keep hold of one of their prized assets.
The Robins' recruitment drive will once again take importance over all aspects, as Rovers once again try to build a new half-back partnership.
