Carr has agreed to a one-year deal with a series of options to make it a four-year deal worth $24 million, a source tells ESPN's Adam Schefter.
Carr, who went a stretch of 36 straight games without an interception before picking off Giants quarterback Eli Manning in the 2016 season opener, is coming off his best season with Dallas, finishing with nine pass deflections, a quarterback pressure, a tackle for loss and 61 tackles with Dallas.
He had six interceptions and two touchdowns in his first two seasons with the Cowboys after signing a five-year, $50 million deal as a free agent in 2012.
A fifth-round pick in 2008 by the Chiefs, Carr has started and played in every game of his career (144 and counting). He turns 31 on May 19, but he's been able to stay relatively injury free.
With Carr agreeing with Baltimore, and cornerback Morris Claiborne expected to sign with the New York Jets, the Cowboys will need to restock their secondary.
Dallas lost two other members of its secondary last week when safeties Barry Church (Jaguars) and J.J. Wilcox (Buccaneers) signed elsewhere.
ESPN's Todd Archer contributed to this report.