Monachino has been the Ravens' linebackers coach for the past six seasons, two of which were spent under then-coordinator Pagano.
Well respected for his work with a string of productive linebackers such as Terrell Suggs, Elvis Dumervil, C.J. Mosley, Courtney Upshaw and former Ravens Dannell Ellerbe and Paul Kruger, Monachino was a candidate for the Eagles defensive coordinator job that ultimately went to Billy Davis three years ago.
There had been speculation in Baltimore that he would eventually succeed Dean Pees as Ravens coordinator.
Monachino will be charged with turning around a Colts defense that has lacked toughness in big games during the Pagano era.
Owner Jim Irsay conceded at Monday night's press conference that the roster is in dire need of a youth movement. That is especially true on defense, where eight of 11 starters from the past season will be age 30 or older by the start of next season.