Zalewski, 23, was loaned by Roma to Inter in January for the second-half of last season. The transfer became permanent in June.
Inter spent €7m to sign Zalewski outright.
La Dea have now signed the wing-back for €17m, with the deal confirmed this morning.
Zalewski is now reunited with new Atalanta coach Ivan Juric, with the pair together for a short period last season at Roma.
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Internazionale
Atalanta
Nicola Zalewski