Weyman, 28, will finish the current campaign with the Dragons before linking up with the Robins for pre-season training ahead of the 2014 season.
A former Moruya junior, Weyman started his professional career with the Canberra Raiders, making his first grade debut against Penrith back in May 2003.
He spent six years with the Raiders before making the switch to St George-Illawarra in early 2009 where he has picked up a couple of major pieces of silverware.
The prop was part of the side that beat Sydney Roosters 32-8 in the 2010 NRL Grand Final and also played in the 2011 World Club Challenge just months later which saw the Dragons defeat Wigan 21-15 at the DW Stadium.
Rovers’ CEO Mike Smith sees his capture as a real coup for the club.
He said, “Michael is a player of the highest calibre and you only have to look at his record to see that he’s been there and done it at the very top level.
“Meeting him and his agent was a real pleasure and Michael can’t wait to get over to England and get started in 2014.
“As a club, we’ve targeted high quality acquisitions to replace the players who will leave us at the end of the current season and Michael definitely fits that bill.
Meanwhile, Robins’ head coach Craig Sandercock is also delighted that Weyman has been added to his squad, and he added:
“Michael is a big bloke and a class player who will bring a lot of quality and experience to our team. He’ll also provide terrific leadership to our younger players and for them it’ll be a great opportunity to learn from someone who has played consistently at the top level in Australia.”