Green, 34, adds a veteran presence to the Oilers, who are second in the tight Pacific Division race, just three points out of first but just one point ahead of Vancouver.
Green, who has three goals and eight assists in 48 games this season, has played the past five seasons in Detroit, signing there as a free agent after 10 years in Washington, which drafted him 29th overall in 2004.
He is a free agent at the end of this season.
"When you can bring in guys that are only going to help your team, help your depth, and we already know what we got in this locker room right now, just to be able to add to that and be a threat, I think it's fun," Oilers forward Riley Sheahan said.
The Associated Press contributed to this report.