May, who played with the Toronto Maple Leafs at the end of last season, joined the Red Wings on a tryout basis in September. He was sent on a tryout to Grand Rapids of AHL when the Red Wings cut their roster, but they clearly kept their eye on him.
"It was pretty interesting, we had May in a couple of games in exhibition, and no one got hacked or whacked or touched, and then we don't have him and we get run," coach Mike Babcock said, according to the Detroit Free Press. "You get tired of watching it.
"Our guys, I think, do a real good job of competing hard, but we don't have a team that twists off helmets at stoppages, and when you start seeing it all the time, it's just nice when you've got someone to look after that stuff."
May immediately added toughness to the Wings, getting into a fight in his first game Thursday night with Blackhawks forward Radek Smolenak midway through the first period.
"It just gives you a little bit more swagger and he can look after your guys and attack people," Babcock said.
The 37-year-old left wing was picked by Buffalo as the 14th overall selection in the 1990 NHL draft.
May has 127 career regular-season goals, 160 assists and 2,182 penalty minutes. He was on the Stanley Cup-winning Ducks in 2007.
Information from The Associated Press was used in this report.