Sources informed ESPN, CBS Sports and NFL Network of the three-year pact late Tuesday night. McCoy, 32, spent last season with the Carolina Panthers after spending the first nine years of his career with the Tampa Bay Buccaneers.
He signed a one-year, $3 million contract with the Panthers last June.
The 6-foot-4, 300-pound defensive tackle had 37 tackles, 13 quarterback hits, seven tackles for a loss, five sacks and two passes defensed in 16 starts last season for the Panthers. The six-time Pro Bowl selection and 2013 All-Pro had 54.5 sacks in 123 starts during his tenure with the Buccaneers.
McCoy entered the league as the No. 3 overall pick in the 2010 NFL Draft.
The Cowboys lost defensive tackle Maliek Collins to the Las Vegas Raiders Tuesday in free agency. They also lost tight end Jason Witten and safety Jeff Heath to Las Vegas. Dallas lost cornerback Byron Jones to the Miami Dolphins and defensive lineman Robert Quinn to the Chicago Bears.