Cook, who started at center against the Cowboys in Wednesday's preseason finale, will be acquired for a seventh-round pick.
Cook, 29, was a second-round pick by Minnesota in 2006 and he started
40 games for the Vikings before joining the Dolphins last season.
He has recorded starts at right tackle, right guard and center during his career.
"This, really, in my mind, was done for our depth," Jones said on KRLD-FM. "Plus, he's very capable because he's started in several games in the NFL. He is very capable of competing. Hopefully, you'll see him in a lot of games this year."
Phil Costa will serve as the Cowboys' starting center, but he had been slowed by a lower back strain for nearly three weeks. He returned to practice Monday and played 12 snaps against the Dolphins after missing the first three preseason games.
Arkin started the preseason games in Costa's absence, but he struggled at times with his shotgun snaps and penalties.