The Take That star and the 13-strong Liverpool group, who became the first choir to make it through to the live shows of the ITV series in 2018, recorded the festive favourite, written in 1934 by Americans Felix Bernard and Richard Bernhard Smith, remotely over video call.
Since appearing on the talent show the choir have remained close with Williams, sharing the stage with him at Wembley’s SSE Arena and Hyde Park, and featuring on his 2019 album The Christmas Present.
During recording sessions for the song, the 46-year-old encouraged the outfit to be brave amid the coronavirus pandemic.
He said: “Every one of you needs to know we are lions and we are braver than any fear. Fear thinks that it’s bigger than you, but you need to show you’re not scared of it every time and that you’re bigger and stronger than any fear can ever be.
“Think bigger than you ever have and then think bigger again. Without fear, you have no boundaries.”
Williams championed the choir during their time on the X Factor, when he and his wife, Ayda Field, were judges.
He became a co-owner of the LMA, the music, media and performing arts college where they formed, in 2019, alongside founders Richard and Simon Wallace.
Stephanie Wallace-Carr, head of the LMA Choir and creative director of musical theatre at LMA, said: “It goes without saying that this year has been challenging and rocky for everyone in one way or another.
“As a choir, we missed seeing each other every day during lockdown and couldn’t wait to perform together again, so to end the year with a very special duet with Robbie – albeit virtually – is fantastic.
“More than two years after we left the X Factor, we still have an incredible bond with Robbie and we’re so grateful to be able to sing alongside him and hopefully bring a bit of festive cheer to everyone.”
In June, the choir staged a remote performance of Sam Cooke’s Civil Rights-era anthem A Change Is Gonna Come in support of the Black Lives Matter movement.
The group said they aimed to “call for a change and create hope” in the wake of George Floyd’s death in the US.