Federer won his 20th straight match at the tournament and has played in 12 straight Basel finals.
World number three Federer registered a 7-6 (5) 6-4 victory over Copil to claim his 99th career title in front of his home crowd in Basel.
"I'd love to see now what kind of results I can have - but it went his way today, this is how it ended".
Seventh-seeded Daniil Medvedev, who is also in Federer's half of the draw, beat Maximilian Marterer of Germany 6-3, 7-5.
"This was nearly a turnaround week for me", the Swiss legend said.
"The results show it as well, so I'm very happy".
Federer was pushed to the limits in the final as well Copil forced a tie-breaker in the first set before taking a 4-1 lead in the second.
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Federer, 37, spent nearly 90 minutes less on court Saturday than Copil, who has had to come through six matches to reach his second career ATP final.
World No 11 Nishikori's luckless run means that a win in Memphis in 2016, his second career title, remains his most recent.
The first-set tiebreaker was likely to be crucial given Copil's career record of 8-52 when losing the opening set in top-tier matches.
The Japanese's efforts were further undermined by 23 unforced errors and three double faults and though he improved enough to force a second set tiebreak, Anderson held his nerve and sealed the win with an ace.
Despite being broken twice by world number 93 Copil, Federer was never truly in danger, striking 22 winners and winning 32 out of 34 first-serve points.
"It's very hard for me to explain how it feels like".