Lick Digital acquired the company from Prime Active Capital (PAC), which also disposed of its other print interest, the book printer Bell & Bain, last month.
Through the acquisition, Topcopy will temporarily retain its name before integrating into Lick Digital, which is part of a group that consists of Lick Direct, Lick Online and Lick Agency.
The combined Lick Digital business will operate with more than 20 employees and a turnover of £1.5m with the company running from the Topcopy site in Leeds.
Andrew Brown, operations director at Lick Group will head up the new business and said the company was a "great fit" and a move that would allow the group to cross sell to a bigger pool of clients.
"We always keep out eyes open for companies that allow us to improve our service offering and complement what we already offer," he added.
The digital print company runs equipment that includes Xerox, HP and Chromapress machines. Lick Digital's existing client base features HM Prison Services, National Union of Miners and Leeds United FC.
Linden Kitson, group managing director of Lick Group, said: "Lick Digital and Topcopy will work together moving forward to offer an increased proposition of digitally printed services.
"Clients can look forward to ‘business as usual’ throughout the merge of the businesses and of course customer service and quality will be of a usual exceptional standard."