The popular Eastwood High pupil and Explorer Scout, from Newton Mearns, was described as an example to all, loved by everyone who met him.
Reverend Brian More, school chaplain and minister of Newton Mearns Baptist Church, where the service was held yesterday afternoon, led the tributes as around 400 members of his family, friends, fellow Scouts and school pupils listened intently.
He praised Elliot's "vibrancy and quirkiness" and said he was deeply loved by his family and friends.
Stuart Maxwell, Eastwood head teacher, said he had nothing but positive memories of Elliot, who drowned while on the second day of a nine-day Scout trip to Valle D'Aosta, in the Italian Alps.
He said Elliot should inspire everyone to be "a little like him."
Mr Maxwell said: "The one over-riding thought emanating from my memories is that Elliot will live on in our hearts and in our cherished memories.
"He had a positive impact on all our lives. He enriched the lives of everyone who knew him and he made our school a bit better.
"Every day, we should all try to be a little more like Elliot".
He said Elliot "absolutely loved" going to school. "It was the epicentre of his life," he said.
"He had fun and good times with all his friends. Every morning he would arrive before 8.15am to meet his many good friends.
"He had a cheery smile to greet any staff. He was a lovely boy, equally popular with staff and pupils alike."
The head teacher praised Elliot for his contribution to school life, from his interest in playing the guitar to his efforts on the football and rugby pitches.
He added: "If you were in need, Elliot was there to help with support and advice. He was special. Every time we think of him we should smile.
"He was a credit to his school, he was a credit to his parents but, most of all, he was a credit to himself."
His cousin Lauren said she felt as if they "grew up pretty quick together" and that she had seen a glimpse of "the man he was shaping up to be".
Reverend More spoke to Elliot's parents, Scott and Colette, and said they gave him "the life he came to love".
He said: "You gave him that. It's as simple as that. You gave him everything you could, he was your only one".
He said Elliot had been laid to rest shortly before the memorial service "in a quiet moment in a blustery afternoon".
He added: "He was very deeply loved. Coming to Newton Mearns in 2007 was the place where Elliot began to make his life. His sense of humour has never been lost on us, he was great at one-liners."
Mr Maxwell said many of the messages left on tributes to Elliot summed him up perfectly.
One read he was "a treasure to be with", he said, and another paid tribute to someone who "made me happy just to be around".
Counsellors were on hand to support young people after the service.