The 28-year-old Danish Classics specialist returns to Bjarne Riis's team, having stared his professional career with what was then called Team CSC.
Breschel, who won a stage on the Vuelta a Burgos this season and enjoyed top-10 finishes in both the Tour of Flanders and the Gent-Wevelgem, signs from Rabobank.
"At the end of the day, the choice wasn't that difficult, even though I have enjoyed being part of Rabobank," Breschel said. "Personally I have great ambitions, and I'm convinced Bjarne and the team are the right ones to help me move on.
"Over the last two years I have always kept in contact with Bjarne, and now, when I had the opportunity to come back, I wouldn't miss it.
"After all, this team is where I feel at home. I'm super happy to be able to return to Saxo Bank-Tinkoff Bank, and I'm very much looking forward to the coming season."
Riis said: "Ever since Matti left the team a couple of years ago, I have always hoped for him to come back to the team for obvious reasons.
"I know Matti very well, both as an athlete and as a person, and I know what he is capable of on the bike. In peak form I have no doubts that he has the potential to win a spring classic or the Worlds one day, and together we will pursue this goal.
"It will take a whole lot of hard work and commitment, but Matti is eager to start over again after some years marked by injuries. I can only say I'm looking forward to start working with him again."