Alfredsson signed on Friday as a free agent with Detroit on a one-year deal worth $3.5 million US, that includes performance bonuses that could be worth up to $5.5 million.
Alfredsson, 40, made his NHL debut with the Senators in 1995-96 after being selected in the sixth round of the 1994 draft by Ottawa. He won the Calder Trophy as the NHL's top rookie and went on to play in six All-Star games. He has been Ottawa's captain since the 1999-2000 season.
But he wanted a better chance at something he's never won.
"I had not won a Stanley Cup and that's a big priority for me," Alfredsson said. "With Ottawa, I think they're getting closer and closer or definitely going in the right direction and has a really bright future in front of them, but at this stage of career there's not much left. I don't have the time to wait for that."
He added: "This is purely a situation to me where this is about me. This is the decision I make for myself, not for anybody else. It's all about trying to get the Stanley Cup."
The right wing confirmed he was returning to the NHL for another season last week after taking some time to decide in his native Sweden.
Alfredsson has scored 426 goals, 682 assists for 1,108 points in 1,178 games for Ottawa, all franchise records. He has added 51 goals, 49 assists and 100 points in 121 playoff games.
"I think the easiest thing for me would be just to stay in Ottawa, enjoy my last year there and retire an Ottawa Senator," Alfredsson said. "It probably would've been a great ending as well, but it's the ultimate prize and I'm a competitive person. I wouldn't have felt the same drive, I think, in terms of just trying to be the mentor and play it out. Ottawa is going to be a good team next year, as well. I felt I needed a different challenge to do this."
He was finishing up a four-year deal that had a salary cap hit in 2012-13 of $4.875 million US.
The classy veteran, who won Olympic gold with Sweden in 2006, has yet to hoist Lord Stanley's Mug. He will now chase that goal with countrymen Henrik Zetterberg and Niklas Kronwall, among other new Detroit teammates.
"I just really like the way Detroit plays hockey: It's a puck-possession game, it's a push-the-pace game," Alfredsson said. "I just think with the personnel they have throughout their lineup, I could come in and be of help in different areas and be part of something really good.
"I know quite a few of the guys from before, I know their personalities, I know how they play and the culture of Detroit really appealed to me from all the conversations I've had with different players that's been there."
Alfredsson scored 10 goals and 16 assists in 47 regular-season games in 2013 , offensive totals that may have been impacted adversely by the long-term absences of teammates Jason Spezza and Erik Karlsson. He went on to average a point per game in 10 post-season contests as Ottawa made it to the second round of the playoffs.
He was recognized earlier this month by the NHL, winning the Mark Messier Leadership Award.
In addition to the Senators, Boston was reported as another team make a concerted pitch to sign Alfredsson.
Detroit general manager Ken Holland said even he was caught somewhat offguard by Alfredsson's decision.
"I really expected to kind of get a response that he was going to stay in Ottawa and [Alfredsson's agent J.P. Barry] said Daniel was taking some time with his family and was considering talking to some teams and explore what's out there," Holland said. "A lot of this has happened fast."
For their part, the Red Wings followed up the Alfredsson move with the signing of centre Stephen Weiss, who's spent his entire career with Florida.