The 20-times Grand Slam champion was at his clinical best to beat Tsitsipas, creating just two break points – but converting both – to win in 69 minutes.
Federer, who clamed a 99th ATP title at his hometown Basel tournament in October, broke Tsitsipas in the first game of the match and saved two break points at 5-4 to claim the first set in 36 minutes.
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Australian Open semi-finalist Tsitsipas held firm up to 4-4 in the second set before the 37-year-old Federer switched gears to seal the decisive break and close out the victory.
"I don't know if Stefanos was born when I won my first title," Federer joked.
"It's a privilege (to play against potential champions) because I'll be watching them on TV. It was a treat to play Pete Sampras and Andre Agassi. I'm sure Stefanos will have a wonderful career.
Tennis is in good hands regardless if I'm there or not.
Swiss Federer also avenged his shock defeat by Tsitsipas in the Australian Open fourth round in January.
The 37-year-old becomes only the second man to reach a century of tour-level tournament wins after Jimmy Connors, who won 109. Steffi Graf (107), Chris Evert (154) and Martina Navratilova (167) make up the other members of an elite ‘Century Club’.
While his latest ATP victory is obviously a milestone moment, according to Federer, it is not necessarily his most memorable.
“I guess I have a few,” Federer told Eurosport at the post-match press conference. “The French Open in 2009 was a big deal for me. Then, of course, also Hamburg in 2002 when I broke the top 10 and beat [Marat] Safin in the finals — completely out of the blue.
“I think title No.1 was a special one for me,” he continued. “I’m not kidding now if I tell you I was hoping I would not go down as a player to never win a tournament, because I lost my first two quite dramatically.
"So when I came to Milan in 2001, and I beat [Yevgeny] Kafelnikov along the way and [Julien] Boutter in the finals - I think I had match point in the second, lost the second set and went to the third and was able to win it.
“I was just so relieved that I was not going to be that guy who has endless talent and no titles,” Federer concluded.
So, you can imagine today sitting here with 100 how much disbelief there is in between what happened then and now.
Tsitsipas, who will break into the top 10 for the first time on Monday, paid tribute to Federer's achievement in an on court interview after the match.
"Just thinking about it, getting to 100 is completely insane, I don't know how you did that. I'd be happy with 100 (match) wins... I'm joking," he said.
It's an honour playing Roger... I've been idolising him since I was six and watching him on TV, I was just like you guys... I had the biggest smile on my face.
With additional reporting from agencies
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