Garrett released a statement, calling the coaching change a "mutual decision."
"This was not an easy decision because of how highly we regard Scott Linehan as a football coach and as a person," he said. "He and I had some really positive, substantive and open discussions which took place in the latter part of this week, and we ultimately agreed that it would be in the best interest of all of the parties involved if we were to make a change at this position."
Rapoport provided Linehan's statement on the Cowboys' decision:
Rapoport also reported on possible replacements for Linehan:
Linehan joined the Cowboys as a passing game coordinator in 2014 and was promoted to offensive coordinator one year later. He served in the latter role for four seasons.
"We don't anticipate any significant changes on our staff," Garrett added.
However, Cowboys executive vice president Stephen Jones appeared on the same radio station later Monday and said no final decisions had been made about the staff, per Ryan Welch of CowboysWire.
"No, we're a little over 24 hours into this," Jones said about making coaching decisions. "... I think it's a little early to be speculating about players, coaches, anything like that other than I really do think our group overall did a nice job."
Dallas finished the 2018 regular season ranked 22nd in both total offense (343.8 YPG) and scoring offense (21.2 PPG).
Linehan has 13 years of coordinator experience at the NFL level. Along with the Cowboys, he also served in that capacity with the Minnesota Vikings (2002-04), Miami Dolphins (2005) and Detroit Lions (2009-13). He was head coach of the St. Louis Rams from 2006 through 2008.
In those 16 seasons, his offenses ranked inside the top 10 in yardage eight times and the top 10 of scoring on six occasions, per Football Reference.
Linehan's replacement will inherit a high-upside group of playmakers led by quarterback Dak Prescott, running back Ezekiel Elliott and wide receiver Amari Cooper, plus any offseason additions.