The 14-year-old was one of 22 people killed in the terror attack on May 22 2017, with Eilidh's Trust set up in her name.
Music student Fergus Bryce has composed the piece, which will be given a special debut at the National Piping Centre in Glasgow on Friday March 13.
The 20-year-old, originally from Evanton in the Highlands, said he is "really happy" with how the tune has turned out so far.
He said: "The music is specifically written to be optimistic and looking to the future - something that ties in perfectly with the ethos of Eilidh's Trust.
"I hope the listeners will enjoy the tune as much as we have in composing and performing it, and that it adds to Eilidh's legacy in supporting music education for other young musicians.
"Having been drumming and involved in music since I was eight I have benefited from music education.
"Therefore, Eilidh's Trust's ambition for young musicians is something that resonates a lot with me."
He added: "This is why I was very keen to support their work and my studies have proved to be the ideal opportunity to do this.
"I'd like to thank everyone who has supported me in this project, including my fellow musicians and the National Piping Centre for being so accommodating for my event."
Mr Bryce began drumming aged eight and played through school before being part of the National Youth Pipe Band of Scotland and Glasgow Police Pipe Band.
He then went on to win the European Championships, Scottish Championships and World Championships with Inveraray and District Pipe Band at the age of 19.
The tune is different from a song released in 2018 to help the trust raise funds for a memorial to Eilidh, the design of which was unveiled last year.
Work is continuing on the bronze sculpture, which features a young female bagpiper with her pipes at rest, reaching out a hand to a young boy also learning the instrument.
The life-size sculpture by Essex-based artist Jenna Gearing is not based on the teenager's own appearance, or that of any specific individual, at the wish of her family.
It is hoped the memorial will be established on the island later this year, which could also involve Mr Bryce and his musical composition at the unveiling.
Suzanne White, founder and trustee of Eilidh's Trust, said: "We were thrilled when Fergus approached us with his proposal to support the trust in this way.
"What he has composed is a really beautiful piece of music, which captures the true positivity of youth and ambition for the future - things the trust strives to support.
"We look forward to the music event that will not only premiere this composition but will showcase a wide range of young musical talent.
"This is what the trust is all about, supporting our young talent to exploit their skills and enthusiasm to excel in the world of music.
"We cannot thank Fergus enough for his support of other young musicians by boosting our work."