The 25-year-old forward became an unrestricted free agent after he did not receive a qualifying offer by the Chicago Blackhawks. He scored 27 points (14 goals, 13 assists) in 55 games last season for the Blackhawks. He was fifth among NHL rookies in goals and tied for sixth in points.
"I think he filled a need for us," Red Wings general manager Steve Yzerman said Thursday. "He is a skilled guy. He's got good hands. I think he's got good hockey sense. He has some versatility to him as well. So, again, we had a big hole there in the center position for an offensive-minded playmaker."
Suter was undrafted and played in his native Switzerland for five seasons before joining the Blackhawks last season.
Sam Gagner agreed to a one-year contract to remain with the Red Wings on Wednesday. The 31-year-old forward scored 15 points (seven goals, eight assists) in 42 games for the Red Wings last season. The No. 6 pick by the Edmonton Oilers in the 2007 NHL Draft, Gagner has scored 474 points (171 goals, 303 assists) in 886 regular-season games with the Red Wings, Vancouver Canucks, Columbus Blue Jackets, Philadelphia Flyers, Arizona Coyotes and Oilers, and has four assists in 11 Stanley Cup Playoff games.
"He's a very versatile guy for us," Yzerman said. "Last year he really transitioned in his game and remade himself and has become a valuable defensive forward who can play in a lot of different spots for us."
NHL.com columnist Nick Cotsonika contributed to this report