Sagan's Tinkoff teammates Maciej Bodnar, Michael Kolar and Erik Baska, and his elder brother, Juraj Sagan, are also moving to the German team.
"It is a great honour to welcome one of the most popular cyclists of our time in our team," Bora-Hansgrohe team manager Ralph Denk said in a statement.
"That's why we tried to provide familiar surroundings as far as possible.
"I think Peter's trust in us proves that we did a good job (in recent) years and have a solid reputation in the peloton."
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Sagan currently leads the WorldTour rankings and will look to defend the World Road Race Championships in Doha after winning the title in Virginia last year.
Russian owner Oleg Tinkov will withdraw his financial backing of the Tinkoff team at the end of the 2016 season.
In another switch, BMC Racing confirmed that they had signed reigning Irish national champion Nicolas Roche from Team Sky.
Roche, 32, left Tinkoff for Sky in 2015 but was omitted from the team's lineup for the Tour de France after a drop in form.
"We are looking forward to a big season again in 2017 and I think Nicolas will be an asset for us," said BMC General Manager Jim Ochowicz to the team's website (www.bmc-switzerland.com)
"Nicolas is a rider who brings a lot of dimensions with his portfolio, including Grand Tour stage wins and top ten finishes in the General Classification, so we are thrilled to welcome him to the BMC Racing Team family."
"I'm super excited," added Roche. "I think I’ll enjoy the aggressive style of racing."
(Reporting by Sudipto Ganguly in Mumbai; Editing by Neville Dalton and Alison Williams)
