Osimhen equalized for Napoli early in the second half by redirecting in a rebound after Sandi Lovric had put Udinese ahead early on.
"I'm happy for all Napoli fans worldwide," Osimhen said. "No one deserves the scudetto more than Neapolitans - more than us.
"I don't care who scored, I just wanted to get the scudetto."
Napoli moved an insurmountable 16 points ahead of second-place Lazio with five rounds still to play.
Besides the 11,000 Napoli fans inside and 5,000 more outside the stadium in Udine in northern Italy, a capacity crowd of more than 50,000 watched the match on jumbo screens at the Stadio Diego Armando Maradona in Naples.
"Napoli, this is for you," Spalletti said. "There are people here who will be able to get through difficult moments in their lives because they remember this moment. These people deserve all the joy."
In Udine, celebrating fans invaded the field at the final whistle, while in Naples there were fireworks and delirium.
Napoli had a brief lapse during the first half during which Lovric found space within the area for a quick control and angled shot inside the far post in the 13th.
Napoli has dominated all season and didn't lose in the league until getting beat by Inter in January. A 5-1 victory over Juventus nine days later left no doubt that this was the Partenopei's year.
Napoli, though, wasn't even considered a title contender before the season because of the departures of former captain Lorenzo Insigne, club record scorer Dries Mertens and defensive stalwart Kalidou Koulibaly.
But Osimhen has developed into the most dangerous striker in the league, and dribbling wizard Kvaratskhelia has done far more than just replace Insigne on the left wing as one of the biggest revelations in Europe this season.
The title also gives Spalletti the one honor he has coveted most after previously managing Roma and Inter and winning two Russian league championships with Zenit St. Petersburg.
Spalletti's innovative style first showed promise at Udinese nearly two decades ago when he led the provincial club to a fourth-place finish and a spot in the Champions League. Udinese coach Andrea Sottil played under Spalletti at Udinese.
"The fans deserve it," Napoli captain Giovanni Di Lorenzo said, his hair colored in Napoli blue from the locker room celebration. "It felt like we were playing in Naples today."