Atalanta finished third in Serie A to secure Champions League qualification for the first time in the club's 111-year history.
The club from Bergamo also reached the Coppa Italia final.
Gasperini, who took over in June 2016, has agreed a new contract worth around $2.4 million per season that will run to June 2022, Gazzetta dello Sport and Sky Sport Italia reported.
The 61-year-old former Inter Milan, Palermo and Genoa boss had been touted as a possible replacement for interim Roma coach Claudio Ranieri.
But he has reportedly been convinced to stay after receiving guarantees that the club will strengthen for the Champions League and not sell their top players.
Atalanta scored the highest number of goals last season with 77 — seven more than champions Juventus.
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