The move is seen as an attempt by GoDaddy to widen its reach beyond the initial set-up of websites.
GoDaddy Chief Executive Blake Irving said the acquisition will give the company a five-year jump in Europe.
The share prices of Godaddy jumped 2.2 percent in early trading. HEG is one of Europe's largest independent web hosting firms and operates brands such as 123Reg, Domain Factory, Heart Internet and Host Europe.
GoDaddy beat rivals like German Internet service provider United Internet AG (UTDI.DE) and Deutsche Telekom AG (DTEGn.DE) to acquire HEG.
The current owner of HEG is European private equity firm Cinven Ltd [CINV.UL], which acquired the business in August 2013 for 438 million pounds ($560 million).
According to Irving, GoDaddy first tried to buy HEG in 2013, but decided against pursuing the plan due to integration concerns.