The star was honoured for her multi-million selling album, 25, which emerged last year after a long struggle with writer's block.
She was unable to accept the award in person, having played in Zurich, Switzerland, on Wednesday night.
But in a video message, she said he was "very grateful."
"I won it on my last album as well... but I was secretly pregnant, so I didn't enjoy the night too well," she added.
"To win it this time is truly, truly humbling."
