Valverde, who had previously finished on the podium a record six times without winning, edged clear of a four-way sprint for the title to take the rainbow jersey.
He survived the brutal final climb up Hottinger Holl, a 3.2 km stretch with a maximum gradient of 28 percent, beginning the descent to the finish line with Bardet and Woods for company and Dutchman Tom Dumoulin in hot pursuit.
Dumoulin caught the leading group of three riders with about two kilometres to go, but it was the 38-year-old Valverde who fought through, launching into his sprint with about 150 metres remaining and holding off a strong challenge from Bardet.
Dumoulin finished in fourth place with Italy's Gianni Moscon rounding out the top five in Innsbruck.
"It's incredible, after missing it for so many years. It's a victory for the team," an emotional Valverde said.
The Spaniard is the second-oldest world champion after Dutchman Joop Zoetemelk won the title in 1985 at the age of 39.
Valverde had twice finished runner-up at the World Championships, in 2003 and 2005, and won bronze in 2006, 2012, 2013 and 2014.
On Saturday, Dutch rider Anna van der Breggen won the women's road race title, while her compatriot Annemiek van Vleuten won the women's individual team trial earlier in the week.
Australian Rohan Dennis won the men's individual time trial on Wednesday.
(Reporting by Simon Jennings in Bengaluru; Editing by Toby Davis)
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