The 23-year-old died on Sunday 13 December after a dinghy he was travelling in with four other local men capsized in a freak wave. One man survived and swam ashore but the three remaining men have not been found.
The service was held in Iona Abbey, where the former labour leader John Smith was buried four years ago.
Missing at sea
Alisdair Dougall, 19, Davie Kirkpatrick, 23, and Logie Macfadyen, 24, have been presumed dead for several days but there is still no sign of their bodies.
Only Gordon Grant, 33, managed to swim to safety.
The men got into trouble at sea as they returned home after a night out at a dance in the village of Bunessan on Mull.
Their dinghy foundered, possibly after being hit by a wave, in the sound between Mull and their home island of Iona.
Mr Grant, the group's designated driver, was the only member of the group who had not been drinking.
No Christmas cheer
The funeral was a private affair for family and friends of Mr Hay, who had recently filmed an episode of the television show Blind Date.
The programme's host, Cilla Black, has sent a message of condolence to Mr Hay's family.
Coastguards and local people looking for the bodies of the missing men said they will try to bring them back for their families before Christmas.
More than 100 people turned out on Sunday to scour the coastline of the island of Mull on Scotland's west coast - but with no success.
Northern Ireland
Scotland
Wales
England
No sign of Iona capsize victims
(19 Dec 98 | UK)
Community of Iona
Islands of Mull and Iona
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