Last Christmas came out on top ahead of the Pogues track. It is the first time that this song has achieved this feat, having been released in 1984, and written by the late George Michael.
The two songs had been competing with each other for the much coveted spot, with Fairytale Of New York reaching number one last week, peaking at second spot in the UK Charts.
Originally released in 1987, Fairytale Of New York reached top spot in the Irish Charts soon after, but missed out on the Christmas number one for that year, by Pet Shop Boys' Always On My Mind.
Following the death of Pogues frontman Shane MacGowan last month, his widow Victoria Mary Clarke has been campaigning for the song to reach number one at Christmas for the first time.
However, it was Last Christmas who came out on top, 39 years on from its original release, finishing ahead of Eurovision star Sam Ryder's track You're Christmas To Me in second spot, with Mariah Carey's All I Want For Christmas Is You in third.
Noah Kahan's Stick Season, finished in fourth place in the charts, with Elton John & Ed Sheeran's collaboration Merry Christmas taking up fifth place.
Despite this, Victoria Mary Clarke shared a classy message, praising Wham! for their success.
"I love ♥ Wham!!! We love George ♥ Wham!", Clarke wrote.
