Federer dominated the 20th-ranked Medvedev and had his first match-point chance to break serve again at 5-1.
Copil began the match with a break in the third game but lost it in the sixth as Federer levelled the opening set.
Federer has not been beaten at his home tournament since losing the 2013 final to Juan Martin del Potro and emerged with a 7-6 (7-5) 6-4 victory over Marius Copil. "It was dream run for me", Federer said in his acceptance speech, before his fans' ovation brought tears welling in his eyes.
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Federer broke in the second game of the final set but Simon refused to give in and replied in the seventh. As Federer bags his the crown in Basel, his ATP career titles stretch out to 99.
"I played quite good tennis, it was an wonderful week", he said.
The Swiss crowd favourite was never able to comfortably take command against an opponent whom he had defeated in their last six meetings.
Fifth-seeded Kei Nishikori of Japan routed local favorite and top-seeded Dominic Thiem in the quarterfinals at Vienna, Austria, dispatching him 6-3, 6-1 in just 66 minutes.
Federer put the pressure on Simon's serve after battling back from 15-40 down in the 10th game and Simon crumbled with two straight errors.
It is Zverev's 52nd win of the season and a ninth semi-final spot for the world number five, who has already qualified for the season-ending ATP Finals in London next month.
The Romanian aims for a first title after arriving at Basel without a career win over a top-10 opponent.
"It's very hard for me to explain how it feels like".
Copil again showed his steel with an early break in the second set before Federer made another fightback with an overhead victor to break back in the seventh game.