Alfredsson, a 40-year-old All-Star right wing, was captain of the Senators and his decision not to re-sign with the team was a surprise.
"We had a lot of discussions here with our family leading up to this the last few days and it pretty much came down to a selfish decision in terms of I have not won the Stanley Cup," the Swede said.
"I feel with Ottawa, they're getting closer and closer and definitely going in the right direction and have a really bright future in front of them, but at this stage of my career I just don't have the time to wait for that."
Alfredsson, a six-time All-Star who won the Calder Trophy as the league's rookie of the year in 1996, will join a Red Wings roster featuring fellow Swedes Henrik Zetterberg, Johan Franzen, Gustav Nyquist, Niklas Kronwall and Jonathan Ericsson.
Media reports said Alfredsson had signed a one-year $5.5 million deal.
The Red Wings also added former Florida Panthers center Stephen Weiss, who agreed to a five-year, $24.55 million contract.
There were 20 signings in the first hour of free agency, including forward Nathan Horton going to the Columbus Blue Jackets on a seven-year contract.
Horton had spent the past three seasons with the Boston Bruins and is facing time off for shoulder surgery in the off-season.
Ottawa responded to the loss of Alfredsson by acquiring left wing Bobby Ryan from the Anaheim Ducks in exchange for wing Jakob Silfverberg, prospect Stefan Noesen and a first round pick.
The Senators also brought in left wing Clarke MacArthur on a two-year deal after he scored eight goals and 20 points for the Toronto Maple Leafs last season.
Toronto, meanwhile, agreed to deals with center Tyler Bozak and right wing David Clarkson. The highly sought Clarkson signed a seven-year deal worth $36.75 million. Bozak accepted a five-year, $21 million deal.
The Edmonton Oilers snapped up defenseman Andrew Ference on a four-year deal, reported to be worth $13 million.
The 34-year-old Ference, born in Edmonton, entered free agency after playing with Boston for seven seasons.
Forward Ryan Clowe moved from the New York Rangers to the New Jersey Devils on a five-year deal that will net him $4.85 million per season. Finnish forward Valtteri Filppula accepted a five-year, $25 million contract with the Tampa Bay Lightning.
The Boston Bruins, defeated by the Chicago Blackhawks in this season's Stanley Cup finals, were busy making deals of their own with a 'blockbuster' trade with the Dallas Stars.
The Bruins signed forwards Loui Eriksson, Reilly Smith and Matt Fraser and defenseman Joe Morrow from Dallas for centers Tyler Seguin and Rich Peverley and defenseman Ryan Button, the teams announced on Thursday.
Phoenix also was busy, signing center Mike Ribeiro to a four-year, $22 million deal and keeping forward Lauri Korpikoski with a multi-year deal.
The Philadelphia Flyers agreed to an eight-year, $64 million extension with center Claude Giroux and added goaltender Ray Emery from Chicago with a one-year deal.
Kazakh goaltender Evgeni Nabokov is staying with the New York Islanders after accepting a one-year contract.
The Carolina Hurricanes agreed to a one-year deal with former Boston goaltender Anton Khudobin and signed defenseman Mike Komisarek on another one-year deal after Toronto allowed him to enter free agency.
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