Allan Kerr, who owns Baskerville Press in nearby Salisbury, bought the firm from managing director Rob Fryer, who is to quit the company next year.
Warminster Press has a staff of 10 and a turnover of £400,000 from four-colour work for designers. It runs a two-colour GTO and four-colour Heidelberg Printmaster and produces educational print.
Fryer said Kerr intended to relocate Warminster to the Baskerville Press' base 21 miles away.
Kerr, who also owns the Cumbria-based printer Finger Prints, said: "There will be no job losses or enforced salary reductions, and existing customer relationships won't suffer."
Warminster Press was formed in 1919 and is a specialist in printing and finishing.
Baskerville Press owner to buy Warminster press
A key industry player has added to his stable of print companies by taking over the 89-year-old Warminster Press.