The England Under-21 worldwide, 22, was part of Vitesse Arnhem's Dutch Cup winning side last season, scoring 10 goals in 33 league games.
Boro had been keen to keep Marten de Roon, who played in the opening game of the season, but they will have to do without the central midfielder this season.
Atalanta finished fourth in Serie A under Gian Piero Gasperini last season - above Inter Milan, AC Milan and Lazio - to qualify for the group stage of the UEFA Europa League.
Boro manager Garry Monk can't understand why the transfer window goes into the season
"They have played an incredible season, the best ever, and what they have achieved last season was insane".
Baker has struggled for game time at Chelsea, but impressed for England's under-21 side over the summer.
Aston Villa were credited with an interest, while offers from unnamed Premier League clubs are said to have been discounted amid fears over a lack of regular playing time.
Boro have been busy during the transfer window, with Cyrus Christie, Jonny Howson, Martin Braithwaite, Britt Assombalonga, Darren Randolph and Ashley Fletcher all joining the Riverside Stadium side.More news: Robert W. Baird Reiterates "Outperform" Rating for Vantiv, Inc. (VNTV)
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