The Bergamo side, Inter Milan, AC Milan and Roma all went into the final round of fixtures in contention for the final two spots.
However, it was Atalanta and Inter, in third and fourth at the start of the day, who triumphed.
Atalanta went a goal down to their rivals early on but fought back to win 3-1 after Sassuolo had their scorer Domenico Berardi sent off for his part in a brawl at the end of the first half.
Atalanta had in the previous two seasons flirted with the Champions League spots, having previously finished in mid-table positions since their last promotion from Serie B in the 2010-11 season.
The club, with a modest budget, finished seventh in 2017-18 and fourth in the previous campaign, however only three Champions League spots were awarded to Italian sides back then.
Next year, the side will make their debut in Europe’s premier competition.
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