Dewey, who was part of the Plate winning Scotland 7s squad at the Rugby World Cup Sevens in Dubai, has scored 20 points in 13 appearances for the senior Scotland team.
On his forthcoming return to Scotland, Dewey said: "I'm looking forward to returning to Scotland and joining Glasgow.
"Glasgow have been on the up for the last three seasons now and their win over Toulouse in France back in January really shows that they are a team to be reckoned with. It's too good an opportunity to miss out on.
"It's going to be tough to earn a place in a very competitive Glasgow back-line, however, I'm looking forward to the challenge.
"I also believe in the importance of being in Scotland, in front of the national coach, for getting myself back into contention for future Scotland honours."
Glasgow Warriors head coach, Sean Lineen, added: "I've always liked the way Rob plays. He has a very big physical presence.
"With Chris Cusiter joining the club in the summer and Thom and Max Evans re-signing until after the next World Cup, Rob is yet another exciting addition to a pretty special looking Glasgow back-line."
Rob originally played for Edinburgh from 2005-2007 before accepting an offer to join Ulster. He will return to Scotland to become a Warrior.
In addition to his 13 appearances at Test level, Dewey has represented the Scotland 'A' team, the Scotland 7s team as well as Scotland U18, U19 and U21.
The 6ft 3in, 17st centre was named Scotland's MVP (most Valuable Player) at the 2008 Barclays Churchill Cup in North America having played in all three games on the tour. He found the score-sheet in the second pool match against Argentina en route to the final against England Saxons in Chicago.
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