Federer and Stan Wawrinka had won their singles matches on Friday, before Italy won Saturday's doubles encounter.
But Federer's 6-2 6-3 7-6 (7-4) success over the Italian number one meant the Swiss took an unassailable 3-1 lead.
In the final, they will meet France, who clinched their semi-final against the Czech Republic on Saturday.
Italy's Andreas Seppi beat Federer's team-mate Michael Lammer 6-4 1-6 6-4 in the final dead rubber, giving the Swiss a 3-2 victory.
Switzerland have never won the Davis Cup, but were losing finalists in 1992, while France are nine-time winners (most recently in 2001) and seven-time runners-up (most recently in 2010).
Federer won the first two sets with relative ease, and although he needed a tie-break to clinch the third, the partisan home crowd erupted with delight as the 33-year-old carried them to their first final for 22 years.
Appropriately, he was then carried on the shoulders of his delighted team-mates on a lap of honour around the Palexpo arena.
"It's nice sharing the emotions with your fans and team members," he said.
"It was a pretty quick court, so if you're not serving so well there are always going to be errors - it wasn't the best performance for either of us.
"Some of the best match-ups I've had have been against France, but we're very pleased to be in the final."
With France leading 3-0 after the doubles at Roland Garros, the Czechs pulled a point back when Jiri Vesely beat Julien Benneteau 6-4 6-3 in the first match of the reverse singles, which were contested over three sets.
However, Gael Monfils defeated Lukas Rosol 5-7 6-4 7-5 to ensure the French ran out 4-1 winners.
The final takes place in France from 21-23 November.
Source - http://www.bbc.com/sport/0/tennis/29197690
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