The 'Foundations' singer debuted a free download of the song - featuring boyfriend Ryan Jarman of The Cribs and his bandmate and brother Ross - on her My Ignorant Youth blog yesterday (December 24).
The trio's take on the Wham! track was accompanied by a message that read: "Merry Christmas Eve! A gift from us to you. Hope you enjoy listening, we enjoyed making this Christmas Number One!"
Ross revealed on Twitter that the song had been recorded in his garage.
Nash has this year embarked upon a UK tour, established her own record label and launched a school songwriting scheme.
She is expected to release her third studio album in late 2012.
> 'TOWIE' cast's Christmas single 'Last Christmas': Watch the video
> The Cribs ready to record fifth album
Listen to Kate Nash, Ryan Jarman and Ross Jarman cover 'Last Christmas' below: