The festive classic was streamed 9.2 million times over the last week, knocking LadBaby's Don't Stop Me Eating off the top spot.
First released in December 1984, George Michael and Andrew Ridgeley's song was held off the top spot by Band Aid's Do They Know It's Christmas?
Ridgeley said he was "somewhat amazed" the record had now reached number one.
He said he was "delighted" and "profoundly pleased" at the news, "albeit 36 years after its first release which is, perhaps more than anything, a testament to its timeless appeal and charm".
"It is a fitting tribute to George's song-writing genius and one of which he would have been immensely proud and utterly thrilled," Ridgeley added.
Since the song was released in 1984, it has returned to the top 10 a further six times.
Fans had previously launched a campaign to get it to number one in 2017, to mark the first anniversary of George Michael's untimely death on Christmas Day 2016.
But it only reached number two - and was thwarted by Ed Sheeran's Perfect.
Its lyrics also inspired Dame Emma Thompson to write the movie Last Christmas, which was released in cinemas last Christmas.