The 20-year-old joined the Swans in January 2015 but struggled to work his way into the plans of Garry Monk and has now been deemed surplus to requirements by Francesco Guidolin for the foreseeable future.
Grimes is hoping that his time with Blackburn helps him to gain some valuable experience, and he could make his debut for the club in Tuesday's Championship clash against Fulham.
"I'm hoping to get some games under my belt in the Championship and I'm hoping that I can help this massive club climb up the league table," he told Blackburn's website.
"It is such a good level and such a big club, getting games in the Championship is my priority at this moment in time and I couldn't think of a better club to be doing it at."
Grimes, who is an England Under-20 international, has made just seven appearances for Swansea.