"To come back after so long away and be so warmly received means so much," she said.
The star, who closed the show by performing When We Were Young, also received best British single and the Global Success award.
The show also featured an emotional tribute to David Bowie, led by Annie Lennox and his friend Gary Oldman.
Lennox called Bowie, who died of cancer last month, "a quintessential visionary" and "the ultimate iconoclast."
