The Cowboys are yet to make an official announcement regarding Linehan's hiring, but he is believed to have taken part in the team meetings yesterday.
His addition means that Dallas are likely to have a third different play-caller in as many years, with offensive coordinator Bill Callahan expected to have those duties stripped off him having taken them over from head coach Jason Garrett for the 2013 season.
Linehan has worked with Garrett before as they both acted as assistants with the Miami Dolphins in 2005, and the 50-year-old has spent the last five seasons with the Lions.
He will now call plays for an offense that finished fifth in the league last season in scoring but struggled for yards, posting their lowest total since 2005.
Linehan's Lions overwhelmed the Cowboys defense in October as quarterback Matthew Stafford threw for 488 yards and Calvin Johnson caught 14 passes for 329 yards - the second highest single-game total in NFL history.
They also made a total of 623 yards on offense, which was the most that the Cowboys had ever allowed in an NFL game before the New Orleans Saints gained 625 later in the season.