The centre will be established at the city's newest industrial estate, which is being created next to the busy M74 extension.
BT has agreed to lease the facility, which will house around 50 staff.
Building work is due to begin in May and is expected to be completed before the end of the year.
It's another boost for Clyde Gateway, which is tasked with breathing new life into the cash-starved East End.
The new 35-acre Clyde Gateway East business park is being created in partnership with Glasgow-based property developers Scot Sheridan.
Costing £35m, the estate on wasteland at Auchenshuggle, next to St Peter's Cemetery on London Road, will eventually house more than 1000 workers.
BT Scotland official James McClafferty, said: "This is the ideal location for us, providing a technical base for engineering operations close to our customers and with significant external space that we can use for practical purposes.
"As a major employer in Glasgow, with some 2000 staff in the city, we're looking forward to moving in to this additional accommodation and supporting the important, ongoing regeneration of the Clyde Gateway area."
A number of firms have already moved on to the industrial park and the impending arrival of BT is welcomed by Clyde Gateway chief executive Ian Manson.
He said: "It is incredibly encouraging that companies with the status of BT are investing and locating here in the east end of Glasgow.
"It is especially pleasing that they will be occupying a site which, until our intervention back in 2009, had lain derelict for almost 30 years."