The Snowman and the Snowdog is a sequel to the Oscar-nominated original and marks 30 years since the first film aired.
Burrows and Eshkeri recorded the score at Abbey Road Studios earlier this month with the London Metropolitan Orchestra.
The 60-piece orchestra were joined by a choir featuring Emmy the Great, Edith Bowman, All Angels, Celia Graham and musical backing from Ash's Tim Wheeler and Dom Howard from Muse.
'Light the Night' is the official single for the film, which will accompany the flying sequence featuring the Snowman and the Snowdog. In the original, Aled Jones's 'Walking in the Air' was used.
Burrows left Razorlight in 2009 and has had a successful solo career with albums Company and Funny Looking Angels.
"It was a huge honour to be asked to write the music with Ilan for The Snowman and the Snowdog," said Burrows.
"When he first rang me and told me, I dropped the phone. It's a total dream come true for me. The new film has all the magic of the original and fills you with festive warmth, but floors you and has you in tears at the same time. Working with the same team who were responsible for the original film has been such a fantastic experience."
Watch 'Walking in the Air' from the original Snowman below:
Eshkeri added: "The Snowman is an institution in the UK and I am incredibly excited to be involved in the sequel. The music is an iconic part of the film as, without dialogue, it helps to tell the story by expressing the characters' emotions."
'Light the Night' will be available for download from December 10. The official soundtrack for the film follows on December 17.
The Snowman and the Snowdog will premiere on Channel 4 at Christmas.