Tthe 17-time grand slam champion sailed to a 6-4 6-2 6-2 victory over Richard Gasquet in Lille on Sunday to earn his team an unassailable 3-1 lead in the final.
Federer, who recently sat out the ATP World Tour Finals decider against Novak Djokovic through injury, said the triumph should be enjoyed by colleague Stanislas Wawrinka and the rest of the Swiss team.
"Everybody worked incredibly hard to get me match-ready, and Stan has put in so much effort over the years and he played an unbelievable weekend," he said. "That's what gave me the opportunity today.
"I'm very much aware of that and this one's for the boys. This is not for me, this is for them.
"I've won enough in my career that I don't need this to complete everything - ticking the boxes. I'm just happy for everybody else.
"I'm happy we can live a great historic tennis moment in our country."
Gasquet was a late replacement for the injured Jo-Wilfried Tsonga, but Federer was pleased with the way he was able to adapt under the circumstances.
"I'm very happy with the way I played," he added. "Clearly, I expected Jo to be on the other side of the net, but I was able to understand the change.
"I had an hour to get ready. Things weren't easy out there, but I was able to play aggressive tennis and I'm happy it paid off."