Watson, from Salford, Greater Manchester, launched his classical career after he was spotted singing Nessun Dorma in a local working men's club.
"I can't begin to explain how much this award means to me - well it's a very, very long period of hard work," he said.
"Before this, the only thing I won was the egg and spoon race, aged seven."
Watson, from Salford, Greater Manchester, launched his classical career after he was spotted singing Nessun Dorma in a local working men's club.
Conductor Simon Rattle won three awards - one for Outstanding Contribution, and two for an album of Mahler's 10th Symphony which he recorded with the Berlin Philharmonic Orchestra.
Sir Simon, who will be taking over as chief conductor of the Berlin Philarmonic in 2002, told the audience that, though Britain was in the middle of an election: "I must have missed the reference to the arts from any of the parties."
He added that he wanted to thank the critics for "keeping the arts in the public eye".
ITV newsreader Katie Derham hosted the award ceremony, held at London's Royal Albert Hall.
Other winners included Nigel Kennedy (who now prefers to be known simply as Kennedy) who was named Male Artist of the Year, Female Artist of the Year Romanian soprano Angela Gheorghiu and Freddy Kempf, 23, winner of the Young British Classical Performer award.
Criticism
All-girl string quartet Bond, clad in skintight leather outfits, opened the awards with an updated rendition of part of Vivaldi's Four Seasons.
The choice of the quartet had attracted some criticism, even from within the Classical Brits judging panel.
Kennedy was rewarded with rapturous cheers when he played an eastern folk song - and at one point serenaded a woman from the audience.
This year's ceremony is only the second for the Classical Brits, which has been trying to tread the fine line between the pop-crossover world of artists like Bond and Vanessa-Mae and what is seen as the more purist world of the classical mainstream.
The awards will be broadcast on ITV on 3 June.
Classical Brits winners 2001:
Male Artist of the Year - Kennedy
Female Artist of the Year - Angela Gheorghiu
Ensemble/Orchestral Album of the Year - Mahler: Symphony No 10 - Berliner Philarmoniker/Rattle
The Critics Award - Mahler: Symphony No 10 - Berliner Philarmoniker/Rattle
Young British Classical Performer - Freddy Kempf
Rover Album of the Year - Russell Watson, The Voice
Best Selling Classical Debut Album: Russell Watson, The Voice
Outstanding Contribution - Sir Simon Rattle