The Bianconeri will pay €15m in four instalments for the 22-year-old, with an extra €6m in bonuses dependent on certain conditions being met during his time in Turin.
Caldara will be loaned back to Atalanta for 18 months before beginning his Juve career in the summer of 2018. He has penned a deal until 2021 with the reigning Italian champions.
On Wednesday, his team-mate Roberto Gagliardini joined Inter in a €25m deal and midfielder Franck Kessie has been the subject of regular transfer speculation.
Caldara, a centre-back, has scored three goals in 11 games in Serie A this season. Known for his intelligence and serenity, he has been compared to Juve veteran Andrea Barzagli.
Atalanta have not finished in the top half of the Serie A table since their most recent return to the top flight for the 2011-12 season.
Caldara is Juventus' second first-team signing of the month following the arrival of Genoa midfielder Tomas Rincon for €8 million.