The track about Faulkner, who died last summer, is called My, My, Time Flies, and features a guitar contribution from Faulkner's old onstage sparring partner Pat Farrell.
The pair played together for many years in the Floating Dublin Blues Band and Farrell was once married to Enya's big sister, Moya Brennan of Clannad.
The track was the last one recorded for the highly anticipated CD, which is scheduled for release on November 7, in Ireland and November 10 in the UK.
The song was completed just in time for a special launch party held in London this week and attended by representatives of Warners from all over the world, as well as selected media, including key Press, radio and television personnel.
"We had 11 tracks done," producer Nicky Ryan revealed. "But we just wanted to do something for Jimmy.
He was one of the great unsung heroes, a really unassuming guy and a great guitar player.
"There's a lot of them out there, and so it was something we felt strongly about. So it became the final track."
Played separately at the launch, as it had not yet been slotted into the album's running order, it is believed to be a real departure for Enya, featuring a sweet guitar solo by Pat Farrell.
Enya herself said: "We only just finished the record, so I'm really excited about it. It's all so fresh, it's brilliant."
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