Five Fables won best app at the first day of prize ceremonies at the festival in Inverness.
Heaney drew on the work of 15th Century Scottish poet Robert Henryson for the five morality tales.
They were adapted for a TV animation by Northern Ireland's Flickerpix which was narrated by Connolly.
Among Five Fables is The Two Mice, a story about a town mouse and a mouse from the countryside.
Heaney, who died in 2013 at the age of 74, was acclaimed by many as the best Irish poet since WB Yeats.
He was awarded the Nobel Prize for Literature in 1995 "for works of lyrical beauty and ethical depth, which exalt everyday miracles and the living past".
David Cumming, of Waddell Media which runs the Flickerpix, collected the festival accolade on Wednesday on behalf of the animation studio and Touch Press.
He said: "It's very exciting to win this award.
"I think the whole Celtic media industry is really unusual, because it's very diverse and very eclectic.
"It's one of the last places in television where not everything is absolutely ratings-fixated, and that you can still get commissions to do quite strange, out-there stuff, which I think really encourages creativity."
Dolores Keane: A Storm in the Heart by RTE/Scratch Films won the arts award and The Hunchback in the Park by BBC Cymru Wales took the animation prize.
Independent production company Move on Up's Katie Morag was named best children's television series.
Adapted from Mairi Hedderwick's books of the same name, episodes of Katie Morag have been shown on CBeebies, CBBC and BBC Alba.
The books tell of the adventures of a feisty, independent, red-haired girl who lives with her family on the fictional Scottish island of Struay.
Cherry Campbell from Glasgow plays Katie Morag in the TV series.
Winner of the entertainment category was Welsh comedy series Dim Byd, which is produced by S4C and Cwmni Da.
TG4 and Touchline Media won the sports award for Arkle.
The documentary tells the story of Arkle, the Irish horse named after a mountain in Sutherland that became the greatest steeplechaser in history.
A statute in the horse's honour stands at Cheltenham race course.
On day two of the awards on Thursday, BBC Two Scotland's documentary Being Sixteen about 16 and 17-year-olds voting in the Scottish independence referendum won the young people's category in the festival's awards for excellence.

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The winger, 22, was dismissed in the loss to St Johnstone after appearing to react to Stephen Mitchell's award of a foul throw.
Tynecastle head coach Ian Cathro said after the game he would review the incident, but backed his player.
But BBC Scotland has learned the club is not planning to lodge an appeal.
Nicholson will be suspended for Saturday's home match against Dundee.
"I want to see the footage [of Nicholson's red card]," Cathro said in his post-match interview following Wednesday's defeat in Perth.
"I don't think there was any aggression directed in that. I take that quite clearly from how Sam describes the situation and from other players around it. That's something that needs looked at."
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An app based on an TV project involving Scots comic Billy Connolly and the late Irish poet Seamus Heaney has been honoured at the Celtic Media Festival.
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Hearts will not appeal against the red card Sam Nicholson received for an alleged spit in the direction of an assistant referee at McDiarmid Park.