Beach Magazines & Publishing is behind Junior, Junior Pregnancy & Baby, and Wedding Day magazines. A further £1.5m is payable by Future in one year, subject to the business meeting certain targets.
The three successful magazines will continue to be run by founder Chris Taggart as part of Future's Entertainment portfolio.
Junior was launched in 1998 and is targeted at ABC1 mothers of children from 0-8 years old. Junior Pregnancy & Baby is a brand extension of Junior, launched last year.
Wedding Day is a bi-monthly title with an ABC of 31,679, which Beach acquired from Crimson Publishing in May 2003.
Future Publishing's managing director Robert Price said: "We are buying a magazine business, which we believe has significant growth in it. These titles take us into new special-interest areas while playing to our traditional strengths of publishing high-quality and deeply targeted magazines."
Future reported circulation revenue is up 6% for the nine months to September 30 on turnover of £133m.
Growth has come on the back of the acquisition and launch of several new titles.
In August, Future paid £2.5m to acquire PC Zone and Computer & Video Games magazines and the computerandvideogames.com website from Dennis Publishing, while this month Future bought What Laptop magazine from Crimson Publishing for £650,000.
In addition, Future launched a hobby magazine in August and Jetix magazine, in a collaboration with the Jetix children's TV channel, in September, as well as Papercraft Inspirations and HairStyle & Beauty as the company looks to continue expansion of its entertainment group.
Future chief executive Greg Ingham said: "We have succeeded with a number of acquisitions, launched some interesting new titles, and refreshed and improved a number of existing titles."
Future also announced that it was planning to replace the Network from its company name with Plc.
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