U2 frontman Bono, The Edge and Pearl Jam singer Eddie Vedder were among the stars who joined family, friends and fans for the service at St Patrick's Cathedral in Dublin on Tuesday.
Bono addressed the funeral and led the congregation in a singalong of the U2 song Beautiful Day.
With the cathedral full, hundreds more gathered outside to watch the proceedings on large screens which had been erected while more than 40,000 watched a livestream of the funeral.
The funeral featured multiple musical tributes as well as memories shared by family members.
Tributes poured in from around the world after Hansard, the frontman of The Frames was killed at 56 in a motorcycle crash on the outskirts of Dublin on July 29, hours after taking part in a trad session at The Wren's Nest pub.
Hansard featured in celebrated film The Commitments, and won an Oscar for best original song for Falling Slowly in 2008, which he co-wrote with Marketa Irglova for the movie Once.
He began an annual Christmas Eve charity busk outside the Gaiety Theatre 16 years ago, drawing members of the public to see famous Irish musicians perform in aid of the homeless in Dublin.
Hozier, Declan O'Rourke, Jerry Fish and Imelda May were among the first to arrive at the cathedral.
Actors Steve Coogan and Chris O'Dowd were also in attendance, as well as former Sinn Féin president Gerry Adams and traditional musician Finbar Furey.
Breanndan O Beaglaoich read a poem and then described Hansard as a "one-off person the likes of which we won't meet again".
"He was so well-known on the big stages of Ireland and all over the world.
"But to us, who were close to him, he was an ordinary, kind-hearted Ballymun man. A true Dub."
Hansard's wife Maire thanked the emergency personnel who came to her husband's aid following last week's accident.
"I owe my deepest gratitude to all our good friends who have spared no effort to give me to guide me through this time.
"As Glen's wife, I want to thank him for the life we shared, searching for truth and beauty side by side. We found it in our son Christie."
Vedder sang Hansard's The Song Of Good Hope, with Irglova, alongside whom the Dublin musician had won an Oscar.
Bono told the funeral that Hansard had thousands of "best friends".
He then played on his phone a tribute that had been sent to him from American singer Patti Smith following Hansard's death.
At the end of the service, Hothouse Flowers singer Liam O Maonlai led performers and the congregation in a rendition of Bob Dylan's Forever Young.
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