AC Milan and Juventus missed out, while Cremonese were relegated.
Como, who have never participated in any European competition in their 119-year history, were playing in the fourth division just seven years ago.
Four teams were fighting for the final two Champions League berths in the final round.
Milan and Roma were in pole position as they occupied the third and fourth spots. They were level on points, two above Como and Juventus.
While Roma managed to win 2-0 at already-relegated Hellas Verona on Sunday (Monday AEST), Milan lost 2-1 at home to Cagliari. That saw the Rossoneri leapfrogged by Como, who won 4-1 at Cremonese.
Roma finished the season in third place, two points above Como, who managed fourth place and a spot in Europe's elite club competition.
Juventus finished sixth, two points behind Como after the Bianconeri's derby with Torino finished 2-2.
Milan — who were loudly booed at the end of their match — finished the season one point adrift of Como in fifth.
Como, based on the shores of the eponymous lake in northern Italy, have made rapid progress since Indonesian tobacco billionaire brothers Robert Budi Hartono and Michael Bambang Hartono purchased the club in 2019, when they were in Serie D.
The Champions League could prove enough to keep Fabregas at the club, with bigger teams across Europe reportedly interested in the 39-year-old coach, who has impressed in his first senior managerial position.
Elsewhere, last season's champions Napoli beat Udinese 1-0 to finish second, while Lecce defeated Genoa by the same scoreline to secure Serie A safety.
The result saw Lecce move four points above 17th-placed Cremonese, who will join Verona and Pisa in the second division next season.
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