The 32-year-old Australian left Team Sky after two years with the British outfit, with whom he played a key part in Bradley Wiggins's Tour de France victory in July.
Rogers is set to play the same support role for Spain's Alberto Contador, who will seek a third Tour de France win next year.
"I am very excited to be part of an extremely strong and experienced crew such as Team Saxo-Tinkoff in the coming seasons," Rogers told his new team's official website.
"I believe that I can have a positive effect on the team, especially in stage races ranging from the shorter stage races to the Grand Tours. I'm really looking forward to the new challenges ahead."
Saxo-Tinkoff team manager Bjarne Riis added: "I think Michael's record pretty much speaks for itself. He is without a doubt a world class rider, a very strong time trialist, who is also capable of climbing, and on top of that he is a great guy."
Rogers won three consecutive time-trial world titles from 2003 to 2005.