Cole will likely make his Stars debut Thursday night against a visiting Oilers team that will have Taylor Hall return from suspension.
Before Dallas (10-8-2) posted a 5-4 overtime victory at Columbus on Tuesday night, the club announced the acquisition of Cole from Montreal in exchange for fellow right wing Michael Ryder and a third-round draft pick.
Stars general manager Joe Nieuwendyk called Cole a "top-six power forward." Cole had three goals and three assists in 19 games for the Canadiens after matching a career high with 61 points last season.
"I know (Cole) has got a lot of experience," Dallas coach Glen Gulutzan said. "He's won. He's a direct, big, fast-moving skater. I talked to (captain) Brenden (Morrow) a little bit and he said (Cole) is a guy you don't like to play against."
Ryder had been tied for the team lead with 14 points.
"Ryds will be a missed guy here," Gulutzan said. "He's a good guy and a good player, well-liked by his teammates."
Edmonton (7-7-4) is one of the league's lowest-scoring teams at 2.2 goals per game. The Oilers will welcome the return of Hall, who was suspended the last two games after getting ejected for kneeing Minnesota's Cal Clutterbuck in last Thursday's 3-1 home defeat.
Hall is tied for the team lead with 13 assists and his 16 points are second on the Oilers to Sam Gagner's 18.
The Stars have won six straight over the Oilers, including two victories this season -- both on the road. Dallas is 10-0-1 in the last 11 home meetings since Edmonton's most recent regulation win in Texas on Dec. 8, 2006.
Stars goalie Kari Lehtonen is expecting to return Thursday after missing five games with a groin injury. Lehtonen, who has posted a 1.19 goals-against average in winning his last five starts against the Oilers, was activated from the injured list Wednesday.
The Oilers, meanwhile, have placed Nikolai Khabibulin on injured reserve and recalled Yann Danis from the minors. Devan Dubnyk will start Thursday, and he's 0-4-1 with a 4.01 GAA in five career starts against Dallas.
Edmonton built a 2-1 after 40 minutes as it opened a nine-game trip with Monday's 3-2 overtime loss at league-leading Chicago. Rookie Nail Yakupov ended a nine-game goal drought.
"Big picture, it's an excellent point against the strongest team in the National Hockey League right now," coach Ralph Krueger said. "Of course you feel pain, having the lead going into the third period."
The Oilers continue to excel on special teams with a power-play percentage of 23.8 and a penalty kill at 86.6 percent. They know they must improve at even strength.
"We just stick with it," Krueger said. "That's 17 out of 18 games where have been one-goal games where we've been in them so we gotta believe we're on the right track."