“Being a ballboy really inspired me,” he said. “But I cannot believe that I’ve won here 10 times.
“I never even thought that I would win it once, this has been an unbelievable week for me.”
With his wife, children and parents watching, Federer was presented with a metal sculpture depicting a life-sized hand ready to toss a tennis ball in honour of his landmark title.
Federer broke twice per set against his 20-year-old Australian opponent in a win lasting just over an hour in front of a full-house of 9,000.
Federer defeated the 28th-ranked De Minaur in their first meeting.
“Alex has had a great year,” Federer said. “It’s not easy to win tournaments and he’s done it three times already this year.
“There is more to come for you. As for me, I hope to be back here next year to celebrate the 50th anniversary of this event.”
De Minaur joked that he had his own slender hopes prior to the start.
“I was hoping Roger might just get sick of winning, but that didn’t happen.
“He was too good again, it’s amazing. It was a dream to play him here in Basel.
“It’s been a great season for me, I’ll just keep pushing for bigger and better things.”
Federer’s 10 Basel titles ties the 10 he owns from Halle. He has also won Wimbledon eight times.
Sunday’s final was his 75th win in Basel and extended his win streak at his hometown tournament to 24 matches. His last loss at the event came in the 2013 final to Juan Martin del Potro.
Now, he is just six short of the record 109 ATP trophies held by American Jimmy Connors.
Federer is due to play next week at the Paris Masters, the final event of the regular season before the November 10 start of the ATP Finals in London.
He now owns four titles this season after Dubai, Miami and Halle.
De Minaur was bidding to become the first Australian to ever win the title in Basel.
