ESPN NFL Insider Adam Schefter first reported the deal.
The Ravens will send multiple third-day draft picks to Jacksonville in exchange for Monroe, a league source told Schefter. The deal is still pending a physical.
"It was shocking news," Monroe told The Associated Press. "It came out of nowhere for me. I'm just preparing to make the move. It's a fresh start."
Monroe, 26, was taken by the Jaguars with the eighth pick in the 2009 draft out of Virginia.
He has started 62 games over five seasons, including the team's past 30 games. He was Jacksonville's best offensive lineman this season, getting beat at times as he tried to pick up the slack for struggling guard Will Rackley. Rookie Luke Joeckel, the No. 2 overall pick in the 2013 draft, now will switch from right tackle to left tackle for the Jaguars.
The Ravens have rushed for only 256 yards this season -- the fifth-lowest total in the NFL -- and have allowed 12 sacks through four games.
Monroe likely will replace Bryant McKinnie, who has struggled this season and was involved in a party bus incident last week. McKinnie was benched for the entire 2012 regular season but redeemed himself by starting throughout the Ravens' Super Bowl run.
The Ravens re-signed McKinnie this offseason to a two-year, $6.3 million contract, which included a $2 million signing bonus.
With Monroe in the final year of his contract and the winless Jaguars clearly in the early phases of a complete rebuilding project, it made sense to trade him now and get something in return. If Monroe does break into Baltimore's starting lineup and plays well, it could mean a long-term deal for the former Virginia standout and Plainfield, N.J., native.
"I hope it works out," said Monroe, whose wife is from the Baltimore area. "I've never really been focused on a new contract. I've always just been the same guy, ready to give the best I've got and let everything work itself out."
The Ravens hope Monroe can help an inconsistent line that has had difficulty opening holes for running backs Ray Rice and Bernard Pierce. Baltimore allowed four sacks Sunday in a 23-20 loss to Buffalo.
Ravens coach John Harbaugh didn't single out McKinnie as the problem behind the team's lackluster running game, but it was apparent something had to be done after Baltimore set a franchise record for fewest rushing attempts (nine) against Buffalo. Baltimore also is 28th in the league in rushing, averaging 64 yards a game.
"I think the whole O-line is disappointing right now," Harbaugh said Monday. "There's no one more disappointed than they are right now. We've got to run block better, we've got to pass block better."
The question now in Jacksonville: Who's next? With Monroe gone, the team has just one player on the roster (defensive end Tyson Alualu) from any of the three drafts between 2008 and 2010.
The Jaguars aren't close to being competitive, so it makes sense to try to trade players with value who aren't in general manager Dave Caldwell's long-term plans.
Information from ESPN NFL Insider Adam Schefter, ESPN.com's Jamison Hensley and The Associated Press was used in this report.