The deal is for two years, worth up to $5.5 million, including $2 million guaranteed, a source told ESPN's Adam Schefter.
Cowboys owner Jerry Jones said Morris will have a "substantive" role in the offense but views Darren McFadden as the Cowboys' starting running back. Morris, a former sixth-round pick from Florida Atlantic, became a Redskins fan favorite as a rookie.
Morris, 27, rushed for a franchise-record 1,613 yards as the Redskins captured the NFC East title in 2012. He benefited from the zone read option, but also excelled out of any look in the Redskins' outside zone system.
Redskins GM Scot McCloughan spoke about Morris at the owners meetings Tuesday.
"Good for him," McCloughan said. "He's got a home. I wish it was outside the division. That's OK. We made the decision in-house, but it is what it is. He's a good player. He's a very good person and he's had a good career. But you're always trying to get better, always trying to bring in younger.
"I hope he does a really good job, except for against us twice a year."
Morris' overall production dropped each of the next two seasons but he was still an effective runner.
In his first three years combined, Morris rushed for more yards (3,962) than any back in the NFL except for Seattle's Marshawn Lynch. And the two of them shared the top spot for most gains of 10-plus yards with 110. Morris also rushed for 28 touchdowns in this period.
This past season, Morris finished with 806 yards overall and one touchdown. He averaged career lows in yards per carry (3.7) and yards after contact (1.45).
Morris has the most carries in the NFL over the last four seasons with 1,078.
ESPN NFL Nation reporter John Keim contributed to this report.