The deal will be complete once Monroe passes a physical and the Ravens will send multiple third-day draft picks to the Jaguars for Monroe, according to the report.
Monroe, 26, has started 62 of the past 65 games he has appeared in, including all four games this season since being drafted with the eighth overall pick in the 2009 NFL Draft.
Monroe graded out as the No. 10 left tackle in the NFL last season, according to Pro Football Focus and is scheduled to make $3.8 million this season and $2.562 million in 2014.
BURKE: Joe Flacco’s turnovers, nonexistent run game leave Ravens looking for answers The Jaguars have started this season 0-4, and have the league's worst offense, averaging 7.8 points a game.