According to NFL Network's Jane Slater, the one-year deal is worth $4 million with $2.5 million guaranteed.
The 27-year-old spent last season with the Chicago Bears, amassing 78 tackles, two interceptions (one returned for a touchdown), five pass breakups and two fumble recoveries.
Clinton-Dix began his career with the Green Bay Packers in 2014. He played for the Pack until an October 30, 2018, trade sent him to the Washington Redskins. He then signed a one-year deal with the Bears for 2019 and became a free agent when the new league year began Wednesday.
Clinton-Dix will reunite with his old Packers head coach in Mike McCarthy, who was hired in January.
The former Alabama star ranks highly on the class of 2020 free-agent lists.
On Thursday, Stephen Palazzolo and Sam Monson of Pro Football Focus placed the safety fifth among remaining free agents, noting the following:
"As a former first-round pick, expectations for his play are high but may need to be adjusted to simply ‘solid’ given what he has shown so far in his NFL career. Clinton-Dix makes plays on the football in coverage, which is the most important aspect of safety play, but he can come up lightweight against power and misses too many tackles to be happy with (eight in each of the last three seasons)."
Gregg Rosenthal and Chris Wesseling of NFL.com ranked him 37th on their list of all 2020 free agents, calling Clinton-Dix a "plug-and-play starter who can patrol the back end."
The Cowboys are reshuffling a defense that has welcomed defensive tackle Gerald McCoy but let go of defensive back Byron Jones, defensive end Robert Quinn and others.
Clinton-Dix and the returning Xavier Woods and Darian Thompson figure to be the Cowboys' top three safeties.