"The release of Romo, who turns 37 in April, does not come as much surprise, although it was a move that pained owner and general manager Jerry Jones because of the close relationship he forged with Romo over 14 years," reports ESPN's Todd Archer and Adam Schefter.
Another source who spoke to The Associated Press on Wednesday on condition of anonymity said Romo will get a chance to pursue a starting job elsewhere.
Romo will leave the Cowboys as the franchise leader in yards passing and touchdowns after losing the starting job to rookie Dak Prescott. Dallas' 10-year starter broke a bone in his back in a preseason game last year.
Romo, who turns 37 next month, threw for 34,183 yards and 248 touchdowns, but could never match the postseason success of Super Bowl winners Roger Staubach and Troy Aikman.
The Associated Press and ESPN contributed to this report.