The service went live in the city yesterday with 77% coverage expected by the end of the year and 95% by April.
Three said it had invested around £3.4m improving technology at the top of mobile phone masts around the city and installing ethernet cables to allow faster connections once signals have been picked up.
The infrastructure changes allow the masts to handle more users and transfer data more efficiently.
A spokesman for Three said: "Typical speeds on ultrafast are between five and eight megabits per second.
"A high-definition streaming television service will usually take up between two and four megabits per second so ultrafast should be more than sufficient for the majority of customers."
However, ultrafast is only available on certain devices such as iPhone 5 and iPad mini and others which have dual cell, high-speed downlink packet access.
Paul Smyth, Three's area manager for Glasgow, said: "We want people to get the most out of the internet on their smartphones and mobile devices."
The ultrafast service is also being rolled out in Aberdeen, Dundee and Edinburgh.
Three said it has received more than 400 applications for the 270 jobs it recently announced through an expansion of its Glasgow call centre.