The contract is worth $9.53 million, an average annual value of $3.178 million, according to TSN.
"I felt like I have lots of hockey left in me," Daley said. "I don't plan on going anywhere for a while, so I was excited about the three years. I was excited to hear what [coach Jeff Blashill] had to say about where I would play. He was honest. I have to come in like everyone else and earn my ice time. That's all I've expected from anywhere I've went. I'm looking forward to the opportunity and the challenge of knowing what Detroit brings. The league is tough. All of the teams are pretty good now. It's hard to win in this league today."
Daley, 33, had 19 points (five goals, 14 assists) in 56 games with the Pittsburgh Penguins last season and five points (one goal, four assists) in 21 Stanley Cup Playoff games to help Pittsburgh win its second straight championship.
"Pittsburgh has been so good to me over the past two years," Daley said on Sportsnet. "Leaving the group of guys we had was obviously a tough decision. [I'm] off to a different challenge and we will see how this one goes. I'm looking forward to it."
Daley was traded to the Penguins by the Chicago Blackhawks on Dec. 14, 2015. Chicago had acquired Daley from the Dallas Stars on July 12, 2015. Daley spent 11 seasons with the Stars, who selected him in the second round (No. 43) of the 2002 NHL Draft.
Daley has 278 points (78 goals, 200 assists) and 580 penalty minutes in 894 games during 13 seasons with the Penguins, Blackhawks and Stars.
"We think Trevor is really going to be able to improve our defense and make our defense more mobile and deeper," Detroit general manager Ken Holland said. "He can play left defense, he can play right defense. He can go back and get the puck, he can snap a pass, and at the same time, he can also transport it and join the rush. We think that Trevor is also adding some elements to our team that we needed."
The Red Wings also signed defenseman Luke Witkowski to a two-year contract. The contract is for one year and $750,000, according to the Detroit Free Press.
"Luke not only playing defense, but has also played some forward, so we think in Luke we're adding a player that gives us versatility," Holland said. "He can play on the back end and can also go up and play right wing. He played for Coach Blashill for one year at Western Michigan. He brings a physicality and a physical presence to the lineup, something that we also wanted to add after trading away Steve Ott at the deadline."
Witkowski had four assists in 34 games for the Tampa Bay Lightning last season.
"I would like to do whatever is best for the team," Witkowski said "For instance, last year we had some injuries at forward, right wing. I slid up and I felt very comfortable. Some games I'd be going one shift playing right wing, next shift I was playing right [defenseman]. The transition is not as difficult for me personally, others may be. It just feels like somehow I can make that change and I feel comfortable doing it. I like playing both positions. I think my skating helps me be able to do that. As far as where I'm going to start, who knows? I got to earn my spot on the roster and I'm looking forward to doing that."
Daley and Witkowski each said they were looking forward to playing the first season in Little Caesars Arena.
"When I was talking to Kenny, that was brought up with us, to be going into a new building," Daley said. "New building means new dressing room and new accommodations for the players. We get excited for stuff like that too. [I'm] definitely excited for the new place."