"I am just so happy right now," Federer tweeted with a picture of him holding the glittering trophy aloft amid celebrations.
The Swiss ace also posted a series of photos of him failing to hold on to his emotions and one with all the ball boys with "party" written on it.
On Sunday, Federer was at his usual best as he defeated the Aussie 6-2, 6-2 to register his 103th singles titles of his career.
Playing in front of his home crowd, the 38-year-old played attacking tennis against the 20-year-old, who was going for his fourth title of the season.
"It was fast, but very nice. I think I played a great match. It was a tough opener, in the beginning, the first five games, we had some great rallies. I never looked back," Federer was quoted as saying by the ATP Tour website.
"I was great on the offence, made very few unforced errors and came up with the big shots and served well when I had to," he added.
The Swiss maestro also praised his Australian opponent and said: "I thought Alex played a great tournament as well, and I think we both can be very happy. But what a moment for me to win my 10th here in my hometown of Basel."
Federer will receive 500 ATP Ranking points and 430,125 euros in prize money.
( With inputs from IANS )