The 29-year-old has signed what is believed to be a two-year deal with Florian Kohfeldt's side, where he will wear the No.17 shirt.
"The talks with the owners and the coach were very good," he said. "Werder are a big club, where you have the feeling something is growing. I'm looking forward to being part of it."
Kohfeldt said: "I don't think there's much more to say about the qualities of Nuri. He has experienced almost everything in the Bundesliga, been a champion and cup-winner with Dortmund and played for Real Madrid and Liverpool.
"He has the potential to improve us further and gives us more options."
Earlier, Sahin had thanked Dortmund and its fans for their support during two separate spells with the club, the first of which began when he joined as a youngster in 2001.
"I'd like to thank the club and the fans with all my heart for the past few years we've had together," he said. "I'm not leaving, because Borussia will always be in my heart.
"I deeply thank [CEO Hans-Joachim] Watzke and [sporting director] Michael Zorc as well as all my coaches, but especially Jurgen Klopp, who always supported me."
Sahin became the youngest player to appear in the Bundesliga, at the age of 16 years and 355 days, back in 2005. He was then the division's youngest goalscorer when he struck against Nurnberg in November that year.
After winning the Bundesliga under Klopp in 2010/2011, Sahin joined Real Madrid, but his time in Spain was blighted by injury problems.
He spent half the 2012/2013 season on loan at Liverpool before rejoining Dortmund, eventually on a permanent deal.
Sahin made 18 appearances in the Bundesliga last term, but the signings of Axel Witsel and Thomas Delaney had seen the Turkey international slip further down the pecking order.