The Rams and Redskins also swapped their fifth- and seventh-round picks in this weekend's NFL draft as part of the trade.
"Adam is a guy who our staff is very familiar with," Redskins coach Mike Shanahan said. "He is talented and has an incredible work ethic. We feel he will fit in our scheme and will help us reach our defensive goals."
Rams general manager Billy Devaney said Tuesday the team had enough depth at the position to make the deal. He said the draft class was loaded with defensive tackles, and the Rams are expected to re-sign backup Gary Gibson to augment a group headed by Clifton Ryan, Fred Robbins and Darell Scott.
Carriker was the 13th overall pick in 2007 out of Nebraska. He missed last season with a shoulder injury. He will be reunited with defensive coordinator Jim Haslett, a former Rams coach.
Devaney said the Redskins have been trying to trade for Carriker for a while.
"The signings we've made the past couple of weeks we thought, you know what, this might be the right time to do it," Devaney said. "Right now it seems like we've got a little bit of depth. I hope we do."
Carriker was a 300-pound defensive end at Nebraska, where he was Big 12 defensive player of the year as a senior. He played tackle in a 4-3 alignment with St. Louis but is likely to move outside in the Redskins' 3-4 scheme. Carricker has 53 tackles, including two sacks, in 31 career NFL games.
"He's never complained and we used him in multiple positions," Devaney said. "He did the best he could, but it hasn't been a great scheme for him."
ESPN.com senior writer John Clayton, ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.