McFadden had interest from other teams but opted to remain with the Cowboys on a deal that will pay him $980,000 this season.
McFadden, 30, was limited to just three games last year because of a broken elbow suffered last offseason. He spent the first 13 games on the non-football injury list, but the Cowboys paid him even though they were not required since he was not hurt in football drills or training.
Dunbar signed a one-year deal with the Rams that included a $1 million base salary and $375,000 signing bonus.
In the Cowboys' final three games last season, McFadden had 24 carries for 87 yards and caught three passes while playing behind NFL leading rusher Ezekiel Elliott.
In 2015, McFadden finished fourth in the NFL with 1,089 rushing yards, despite not becoming the Cowboys' full-time back until the sixth game of the season. He had five games with 100 yards or more and two games with more than 90 as he set a career high with 239 rushing attempts.
The fourth overall pick in the 2008 draft by the Raiders, McFadden's career has been marked by injuries. Before the elbow injury, however, he had played in 32 straight games.
For his career, McFadden has an average of 4.2 yards per carry, gaining 5,423 yards on 1,301 attempts, while rushing for 28 touchdowns. He also has caught 254 passes for 2,114 yards and five touchdowns.