The £125 million arena, which opened on Monday, September 30, has already hosted gigs by Rod Stewart, Fleetwood Mac and Bruno Mars and will welcome acts including Queens of the Stone Age, Miranda Hart, Calvin Harris and Top Gear Live in the coming months.
Matheson says the new 12,000 seat venue, which has been more than eight years in the making, is a game changer that will generate £130 million for Glasgow’s economy every year.
He said: “Glasgow’s already a UNESCO city of music, we love music but having the SSE Hydro here is an absolute game changer.
“This is going to be one of the top five music arenas in the world, putting Glasgow on a par with the O2 Arena in London and Madison Square Garden in New York. It reflects Glasgow’s global reach and our ambitions.
“The building itself is absolutely magnificent, there is a real wow factor when you see the scale of it. For years to come the best artists are going to be attracted here.”
As well as concerts, the Hydro, which was designed by Foster and Partners architects, will also host World Gymnastics in 2015, the opening of the Ryder Cup in 2014 and a number of events for Glasgow’s 2014 Commonwealth Games.
Matheson added: “Next year Glasgow will be in front of a television audience in excess of 1.5 billion people when we host the best Commonwealth Games that there has ever been and the SSE Hydro will be one of the main venues for that.
“Glasgow’s getting used to opening world class venues but this is the real deal.”
John Sharkey, SEC Limited CEO, said: “This building is absolutely unique and I would define it as world class.
“What we’ll be aiming to do is to have much more international content choosing Glasgow as a first city.”