He will be introduced to the media at a news conference on Friday.
Linehan, 42, had emerged as the leading candidate to replace Mike Martz, who was forced to step down early in 2005 because of health problems. Linebackers coach Joe Vitt served as the Rams' interim head coach for the season's last 11 games.
Linehan, the man wanted by Rams' president John Shaw, was hired after being approved by St. Louis owner and chairman Georgia Frontiere during a meeting on Wednesday night. Before going to the Dolphins, Linehan was the offensive coordinator and quarterbacks coach for the Minnesota Vikings from 2002-2004.
In 2003, Minnesota's offensive unit ranked No. 1 overall in the NFL. This past season, Linehan helped the Dolphins to a 9-7 record and significantly upgraded an offense that had ranked among the league's worst in 2004.