Morris replaces Brandon Staley, who departed last Sunday to become the head coach of the Los Angeles Chargers after only one season with the Rams, where he produced the NFL's top-ranked defense.
"I've got a lot of respect for Raheem and what he will bring to the Rams organization," coach Sean McVay said in a statement. "Not only is Raheem a great communicator, he is also an excellent teacher. Raheem's background coaching both offense and defense gives him a unique perspective which allows him to see the field from a 22-man perspective."
The Rams on Thursday also agreed to hire veteran Joe DeCamillis as the team's special teams coordinator. He will be entering his 33rd NFL season, spending the past six with the Jaguars. Former special teams coordinator John Bonamego has been moved into a role as a senior coaching assistant.
Morris inherits a defense that propelled the Rams to a 10-6 season and features star defensive tackle Aaron Donald and cornerback Jalen Ramsey. The Rams' defense ranked No. 1 in efficiency, yards allowed per game and points allowed per game.
Morris took over as interim coach in Atlanta last October when head coach Dan Quinn was fired after an 0-5 start. The Falcons were 4-7 under Morris and finished 4-12.
Morris, 44, spent six seasons with the Falcons as an offensive and defensive assistant before he was promoted to defensive coordinator for the 2020 season.
Morris and McVay have worked together at two previous stops.
Morris spent three seasons (2012-14) as the defensive backs coach with the Washington Football Team, which coincided with McVay's seven seasons in Washington before he departed for L.A. in 2017.
The two also were on the same staff with the Tampa Bay Buccaneers in 2008, when McVay was an offensive assistant and Morris coached defensive backs.
Morris also interviewed for the Falcons' head-coaching vacancy. Atlanta hired Arthur Smith on Saturday.