The purchase of the property is subject to easyHotel obtaining planning consent from the council for the development of the hotel.
The group plans to convert the building into an 84-room easyHotel, which is expected to open in 2017 if plans are given the go-ahead.
Guy Parsons, easyHotel chief executive officer, said: "We are delighted to be investing in the UK's second largest city.
“Along with its six universities and internationally reputed arts scene, Birmingham is also the UK's fourth largest tourist destination, with 34 million visitors in 2014.
“We see significant opportunity for easyHotel to service business customers and leisure visitors to Birmingham's lively events programmes and look forward to building our brand presence in the city.”
The property is situated in the heart of the city centre, 120 metres from the new entrance to Birmingham New Street Station and 500 metres from the Bullring shopping centre and is surrounded by an array of popular shops, bars, restaurants and other local attractions.
Total cost of the purchase and conversion of the building will be approximately £4.5m.