Cologna, 27, became the first Swiss cross-country ski champion in February of this year when he clinched the 30-kilometre pursuit skiathlon at the Nordic world championships in Val di Fiemme, Italy.
Last year, the Graubünden native became the first man to win the Tour de Ski event three times after winning a gold medal in the 2010 Winter Olympics in Vancouver.
He was named top sportsman for 2013 ahead of Stanislas Wawrinka, the tennis player who is ranked eighth in the world.
Last month, the Swiss Ski Federation announced that Cologna, voted Swiss of the Year for 2012, would miss the start of the World Cup season due to an injury to his right ankle.
Gymnast Giulia Steingrubber, 19, won the title of best sportswoman of the year.
Steingrubber won the European championship on the vault in mid-April in Moscow and later finished fourth in the world championship.
Among other awards handed out at the televised event, the Swiss national ice hockey team won the best team of the year award.
The team ended up with a silver medal at the world championship earlier this year after succumbing 1-5 to Sweden in the final game.
Sean Simpson, who coached the squad, was honoured as coach of the year at the award ceremony, which featured an appearance from British pop singer Robbie Williams.