"I'm really excited to get this opportunity at this stage of my career to go for a Stanley Cup and fulfill a longtime dream," the 40-year-old Alfredsson said on a conference call.
Detroit got a $5.5 million, one-year deal done with Alfredsson on Friday afternoon, mere minutes after NHL teams could sign free agents. The Red Wings agreed to terms on a $24.5 million, five-year contract with Weiss a couple hours later.
ESPN.com's Pierre LeBrun earlier reported the deals.
"It's an extremely exciting day in Detroit and for our team," Red Wings general manager Ken Holland said. "We felt we had some needs we wanted to fill. We wanted to get more scoring. We were challenged last year to score some goals.
"Daniel has been one of the great scorers in the National Hockey League and Weiss is one of the tremendous playmakers."
Alfredsson scored 426 goals and had 1,108 points -- ranking in the top six among active players in both categories -- with the Ottawa Senators, who failed to keep their captain for at least another season.
"I made a very difficult decision to leave Ottawa after 18 years and 17 seasons," he said. "I had nothing but great times in Ottawa. I didn't really see myself making a change a week ago, but as we got closer to free agency, thoughts started creeping in."
Weiss, meanwhile, jumped at the opportunity to be a part of a franchise that has played in 22 straight postseasons.
"Coming from Florida and being there for about 10 years, only playing in the playoffs one time, it was pretty easy," he acknowledged.
Alfredsson won the Mark Messier Leadership Award after scoring 10 goals and making 16 assists in 47 games during the shortened season. He won the Calder Trophy as the league's rookie of the year in 1996 and was an All-Star for the sixth time in 2012.
The Swedish star joins a team with several players from his native country, including captain Henrik Zetterberg.
"Zetterberg, I talked to two or three times," Alfredsson said. "He was the one that I bounced ideas around with mostly."
Detroit hopes Alfredsson can help the franchise compete for a championship next season when it moves to the Eastern Conference. He and his contract may essentially end up replacing Damien Brunner and Daniel Cleary, both of whom are unrestricted free agents. Holland is holding out hope he can keep Cleary, but acknowledged Brunner will likely sign elsewhere.
Weiss fills a void as a second-line center the Red Wings needed.
"It was a big part of the appeal," he said.
The 30-year-old Weiss was limited to playing just 17 games during the shortened season in Florida, a year after he had 20 goals and 57 assists for the Panthers. He had wrist surgery in March, three months before the Red Wings wasted no time adding him to the roster.
Weiss, who is from Toronto, has 145 goals and 394 points in his career that began with the Panthers during the 2001-02 season. He had a career-high 61 points during the 2008-09 season and scored a career-high 28 goals the next year.
Florida drafted Weiss No. 4 overall in 2001 while he was playing for the Plymouth Whalers in suburban Detroit.
"It is neat to come back to a city where I played before and watched the Wings, and wondered about playing for the franchise one day," he said. "It's kind of surreal."
Information from The Associated Press was used in this report.
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