The tower, which stands at 127 metres high - the equivalent of more than 30 double decker buses - is capable of rotating 360 degrees, but has spent nearly 80% of its life out of commission.
Science Centre bosses were expecting a rush of spectators for the attraction's opening weekend.
However, one lucky Evening Times reader has already enjoyed a bird's eye view of Glasgow from the top of the tower.
As revealed in later editions of yesterday's Evening Times, Andrew Montguire, a 22-year-old from Parkhead won our competition to be the first person to visit the top of the only building on the planet capable of rotating 360 degrees.
Andrew took his brother David, sister-in-law Claire Pearce and nephew Scott McAulay as his guests for the trip.
He said: "It was a really awesome thing to do. I'd always wanted to go up it. I'd even asked at the Science Centre before and they said it wasn't open.
"So when I saw the competition I entered straight away.
"I used to work at the Crowne Plaza too, so it's always been something I've watched."
Our winner and his three guests were treated to a short history of Glasgow before taking the two and a half minute elevator trip to the top. Then they were able to take in 20-mile views over Glasgow and beyond and explore a virtual panoramic view on iPads and zooming in on different places.
Andrew, who works at the Tesco in Parkhead, said he wasn't put off by the tall building - but one member of his party was.
He said: "My brother is scared of heights. But in the end he loved it and he said he would do it again.
"It's a really great for a family, it's something different to do."
The tower has only been in operation for just over a fifth of its life.
It missed its opening day in June 2001, as well as the visit of the Queen to the Science Centre a few weeks later.
When it did finally open, it was found the glass elevators were too heavy, causing the mechanism to overheat.
Then it closed for two-and-a-half years because one of the ball bearings which took the weight of the whole structure had sunk.
In January 2005, 10 people, including four children, found themselves trapped 150ft in the air when a cable on their lift snapped, sparking a five-hour rescue mission.
However, engineers say there is no risk of any mishaps this time around as they have built in a number of safety features.
An automatic override kicks in when there are high winds above 20 miles per hour which means passengers will be gently brought back down safely.
Tickets to Glasgow Tower cost £4.95. To book tickets call 0141 420 5000 or drop into Glasgow Science Centre.