Organisers of the Emirates Airline Glasgow 7s say that 15,000 tickets – almost half – have been sold for the event at Scotstoun Stadium on May 5 and 6.
The tournament will see 16 of the best teams in the world battle it out within a specially constructed amphitheatre.
Tickets cost just £15 for a day, with all concessions at half price.
A spokesman for Scottish Rugby said: "We have seen a 20% increase in sales on the same time last year, having taken the decision to host the HSBC Sevens World Series in Glasgow rather Edinburgh.
"The city has really embraced the event and it looks like we are going to have a packed stadium.
"We do not have the same capacity as previous years, but that will make for an electric atmosphere in the best traditions of the home of Sevens.
"We want people to get their tickets in advance so they can take advantage of the free shuttle bus service over the weekend but, more importantly, so they do not miss out on what is an incredible couple of days."
Scottish rugby legend Scott Hastings showed off the Series trophy to fans at Scotstoun.
He said: "As a huge fan of sevens rugby, it is a real honour to take the trophy round Edinburgh and Glasgow ahead of the start of the Glasgow Sevens.
"It's been great meeting all the fans, and I have been surprised by how many people have come to meet us today!
"Having been to Dubai, Hong Kong, Las Vegas and Tokyo already this season, and with more than 15,000 tickets sold, Glasgow is shaping up to be a fantastic new venue for the players and the fans."
Scotstoun Stadium will be transformed into a carnival of sevens rugby when the World Series takes over the whole of the Scotstoun compound, which will be fitted with extra stands.
As well as the main arena where the world's best players will showcase their talents, there will be eateries and bars next to the main stand, an autograph zone next to the teams' area and bands, dancers and face painters, along with other entertainment.
Glasgow securing the event, which has been held at Murrayfield in Edinburgh in recent years, is a major coup for the city.
The sevens circuit includes Las Vegas, South Africa, Australia, Hong Kong and Tokyo and more than 200million people around the world watch the series.
There are 16 teams taking part at Scotstoun, including the recently announced invitational teams from Spain, Portugal, Russia and Zimbabwe.
They will be joined by Argentina, Australia, England, Fiji, France, Kenya, New Zealand, Samoa, South Africa, United States, Wales and of course Scotland.
For more info on the tournament see: www.glasgow7s.com