Cook, 28, is 6-foot-1 and has also spent time with the Pelicans, Mavericks, Lakers and Cavaliers. He appeared in 23 total games between LA and Cleveland last season, averaging 3.3 points. He recently was scheduled to work out for the Warriors.
His signing becomes the latest for a Blazers team that continues to bring in free agents with NBA experience. Along with Cook, the list includes point guard Dennis Smith Jr. and forwards Marquese Chriss and Patrick Patterson.
Cook likely has a shot to make the team, but would probably have to beat out Smith to earn a spot on the final roster.
Training camp tips off in a little more than a week. The Blazers have 18 of 20 spots filled.