Gary Arthur, 48, was from the Paisley area, Police Scotland said.
Three occupants of the Police Scotland aircraft died when it hit The Clutha at about 22:25 GMT on Friday. A further five people inside the pub also died.
Emergency services are continuing the operation to recover any remaining bodies. Prayers will be offered at Glasgow Cathedral later.
A further 14 people are being treated for serious injuries.
Police Scotland said in a statement that “the body of a male has been recovered from the scene”.
“The male has now been identified as Gary Arthur, aged 48, from the Paisley area. His family have been informed.
“Extensive efforts continue to recover the remaining bodies from the scene but, due to ongoing safety constraints, this is likely to take some time.”
Gary Arthur’s daughter Chloe, 18, who has played for the Scotland women’s football team and for Celtic women, took to Twitter to thank everyone for their kind thoughts and to pledge that she would make her much-loved father proud.
Chloe Arthur tweeted: “RIP dad. You’ll always mean the world to me, I promise to do you proud, I love you with all my heart.
“Thanks to everyone who has tweeted me, text me etc, means so much, I have the most amazing friends ever.”
Gary Arthur was a regular on the sidelines watching his daughter play at matches, according to Celtic women’s manager David Haley.
A minute’s silence will be held before Celtic’s Scottish Cup tie against Hearts at Tynecastle on Sunday.
Celtic FC and the Scottish Football Association also sent their condolences.
Emergency teams working through the wreckage had two main purposes.
They wanted to be sure they had located everyone who might have been trapped inside and they wanted to recover as much of the police helicopter as they could to help find out what went wrong.
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