Stefano Pioli"s side came into the final round of fixtures knowing a point would be enough for them to finish top ahead of rivals Inter Milan, but after Giroud squeezed the ball home in the 17th minute, a 19th Serie A title never looked in doubt.
Frenchman Giroud stabbed home a second in the 32nd minute after further fine work from Rafael Leao to put Pioli"s men on course for the trophy, without needing to be concerned with how Inter were getting on back at their shared San Siro stadium.
There was no relenting from Milan as Kessie slotted home a third four minutes later to effectively put the game, and title race, to bed before halftime.
After the break, it was party time in Emilia-Romagna, with thousands of Milan fans, who had clearly purchased tickets among the home supporters, celebrating throughout the half as their side never looked in any danger of being pegged back.
The final whistle was greeted with wild scenes of celebration from the club who have waited far too long for a Scudetto for a side of their grandeur, as they finished two points above Inter, whose home win over Sampdoria was in vain.
Milan showed no sign of any early nerves as they took the game to mid-table Sassuolo.
Fikayo Tomori had seen his header cleared off the line and Alexis Saelemaekers" shot was well saved even before in-form Brazilian Leao stole in down the left and squared for Giroud to fire his side in front.
The second was all about the persistence and guile of Leao, who again held off several challenges before squaring for Giroud to score his 11th Serie A goal of the season.
Kessie, who according to widespread reports in Italy was playing his last game for Milan before joining Barcelona in the close season, then side-footed home the third with ease to complete the job.
Veteran striker Zlatan Ibrahimovic thought he had added the icing on the cake with a fourth off the bench late on, but the Swede"s header was ruled out for offside.
It mattered little, with the celebrations already in full swing. Even Pioli himself, who after 19 years as a coach has finally won his first senior trophy, joined in with supporters singing "Pioli"s on fire" in the final few minutes.
Milan"s jubilant supporters swarmed the pitch as the match drew to its conclusion, embracing players and staff at every opportunity, with their wait for another league title finally over.
