Before working for New York last season, Anarumo was defensive backs coach for the Dolphins from 2012-17.
Anarumo was also the Dolphins' interim defensive coordinator in 2015 due to midseason firings. Bengals coach Zac Taylor and Anarumo worked on the Dolphins staff together from 2012-15.
"I've always had great respect for Lou, and I know he is a tremendous defensive coach," Taylor said in a news release. "He's a great fit for what we want to build here in Cincinnati. Lou is an excellent communicator who the players will have great respect for, and he will get the best out of them."
The move comes after a series of failed attempts to put together the final piece in Taylor's coaching staff. Taylor was not officially hired until Feb. 4 due to a rule that coaches with teams still in the playoffs cannot officially be hired. Taylor was previously quarterbacks coach for the Rams, who made it to Super Bowl LIII, where they lost to the Patriots, 13-3.
The Bengals went after Saints defensive coordinator Dennis Allen, who chose to renew his contract with New Orleans instead of moving. They were also unable to get Florida defensive coordinator Todd Grantham, who chose to stay in the college ranks. Other notable names such as Jack Del Rio and Dom Capers didn't work out for various reasons.
Taylor has maintained that getting the right staff in place was more important than the timetable, although he did admit a few weeks ago that the clock was ticking with the NFL scouting combine coming up soon.
"We need to make sure the right people are here coaching these players. There's a lot of really good coaches out there, so we're going to find the right people," Taylor said on Feb. 5. "We're urgent in assembling the right people, but we're going to take our time and make sure that everyone is a perfect fit for this place. We'll take our time with the process, but I have no concerns that we're going to get the right people in this building."
Anarumo is the Bengals' first official defensive coordinator since Nov. 12, 2018, when Teryl Austin was fired midseason. Then-Bengals coach Marvin Lewis took on the responsibilities of defensive coordinator, and while the Bengals showed improvement, they still finished last in total defense and passing defense. They were 29th in rushing defense and 30th in scoring defense.
The Giants finished 23rd in passing defense in 2018.
Anarumo will be the third defensive coordinator for Cincinnati in three seasons, as longtime defensive coordinator Paul Guenther left after the 2017 season to join the Raiders coaching staff.