The 20-time Grand Slam winner claimed a record eighth trophy at the Aviation Club.
"I'm so happy I'm still playing. It's been a long wonderful journey," Federer said. "I've loved every minute. Winning 100 is an absolute dream come true."
The Swiss second seed was untouchable throughout much of the 69-minute final as he gained revenge for his fourth-round Australian Open defeat by the 11th-ranked Greek youngster.
"It's so special to win my eighth here combined with 100," Federer said. "I had tough opponents all the way through -- right up to Stefanos today.
"He's already having a great career, the game is in good hands."
Federer joins Jimmy Connors (109) as the only other man to have won 100 titles.
His 99th trophy came last October at his home event in Basel.
He missed out on his century at the Paris Masters, the ATP Finals and the Australian Open.
Tsitsipas, who will become the first Greek to ever reach the world's top 10 on Monday, paid tribute to his opponent.
"I've been idolizing him since the age of 6... And now sharing the court, it's even better," the 20-year-old said.
"100 is just completely insane -- I'd be happy with 100 wins. Seriously, I'm trying to get there."
Federer had to work hard this week, winning in three sets over Philipp Kohlschreiber and Fernando Verdasco.
Tsitsipas saw the end of an eight-match winning streak as he arrived in the Gulf with the Marseille title from last weekend.
Federer broke in the opening game of the final, but had to battle to claim the opening set.
Tsitsipas saved three set points in the final game before Federer -- who faced two break points -- finished off the set as Tsitsipas returned wide.
In the second, a break in the penultimate game for 5-4 and a service hold a game later were enough as Tsitsipas put a forehand into the net.