The Seahawks will receive a conditional draft pick in the deal, which was announced Sunday.
Michael, 24, was selected by the Seahawks in the second round of the 2013 draft out of Texas A&M, where he had 35 touchdowns in four seasons.
But Michael played sparingly in Seattle over the last two seasons, appearing in just 14 games and rushing for 254 yards while filling a reserve role behind Marshawn Lynch and Robert Turbin. He likely would have been Seattle's No. 3 running back this season behind Lynch and newly acquired Fred Jackson.
Michael previously had acknowledged the possibility that he might be traded, saying last week that he would accept "everything that [the Seahawks] do."
"As long as I have an opportunity to play somewhere, put some good stuff on film and get some things going, I'll be fine with everything that they do," he said. "They blessed me. They drafted me, and that's good enough for me."
Michael had 32 carries for 118 yards in the preseason, but the Seahawks chose to go with undrafted rookie Thomas Rawls, who had 30 carries for 158 yards and a touchdown in the preseason, as their No. 3 back.
The 5-foot-10, 221-pound Michael will join a crowded backfield that includes Joseph Randle, Darren McFadden and Lance Dunbar as the Cowboys prepare for their season opener against the New York Giants.
The Cowboys waived defensive end Lavar Edwards to create roster space for Michael.
ESPN Cowboys reporter Todd Archer and ESPN Seahawks reporter Sheil Kapadia contributed to this report.