The awards, held by the prestigious music magazine in association with Absolute Radio, saw a host of stars being honoured at London’s Grosvenor House Hotel.
Coldplay frontman Chris Martin attended the event and presented former Oasis star Noel Gallagher with the Best Album Award for High Flying Birds.
Florence + The Machine took home Best Video, while Ed Sheeran was named Best Solo Artist.
The magazine’s readers voted The Libertines’ ‘Gunga Din’, their first new song in 11 years, as Best Track.
Queen’s iconic ‘Bohemian Rhapsody was named Classic Single’, tying in with the 40th anniversary of the song, originally released on October 31 1975.
Matt Mason, senior editor of Q magazine, said: “Q magazine and the Q Awards are about seeking out and celebrating great music and the people who make it.
“It’s been an incredibly exciting year for music, particularly in the UK, and today’s winners reflect that.
“It’s thrilling to recognise a band such as Foals, who’ve reached this level of success by continuing to pursue their own unique vision, while the phenomenal impact of Florence + The Machine, Ed Sheeran, and James Bay on both sides of the Atlantic underlines the power of great British pop music.
“It’s an honour to celebrate the careers of so many artists that have genuinely shaped modern music.
“With very different ideas and innovations, Gary Numan, Tony Iommi, Queen, New Order, Duran Duran, Soul II Soul, Mark Ronson, and Noel Gallagher have all achieved the same result: Radically redefining the musical and cultural landscape.
“The fact that so many of them continue to make excellent music only emphasises what a brilliant year it’s been. We look forward to celebrating more great music in Q next year.”