Hundreds lined up outside the Sean Graham bookies on King Street in the city to snap up one of the tickets after they were handed back to Cliftonville after Celtic didn't sell them.
A capacity crowd of 5,000 will pack the north Belfast ground for the Champions League qualifier, which kicks off at 7.45pm.
Cliftonville fan Chris McErlain was one of those lucky enough to grab a ticket.
"I'm over the Moon. I thought I'd missed all my chances but thankfully I hit lucky," he said.
He and his friend had initially missed out on tickets because they weren't Reds season ticket holders.
Celtic fan William Cassidy, a Glaswegian living in Dublin, set off the night before to join the queue.
"I've been here since one o'clock this morning," he told the BBC. I left Dublin at nine (on Monday). It's been great craic all night with the crowds and the Irish people. It's an historic game."
David Begley, a Cliftonville board member, explained the significance of the tie at Solitude this evening. "It is the first time we have played Celtic in a competitive fixture," he said. "The Champions League makes it a very special occasion."
In addition to the tickets, Celtic made a donation of £5,000 to the charity Cancer Lifeline in Cliftonville's name.
Celtic manager Neil Lennon presented the donation before his media conference in Belfast.
Celtic chief executive Peter Lawwell said: "We are delighted to make this donation to Cancer Lifeline.
"We know this is a charity dear to the heart of Cliftonville and we are delighted to make such a significant contribution."
A spokesman for Cancer Lifeline thanked Celtic for the "very generous donation".
He said: "The finance will help bring vital services to those individuals and their families coping with cancer."
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