The title, which was previously published 10 times a year by Rare Publishing, will expand from 68 to 100 pages with more topical features covering local culture, personalities, shopping and resorts.
It will target the 4.5 million travellers expected to use the airline this year - an average of 750,000 per issue. It will be edited by Ginny Cummings, who previously edited Australasian travel magazine Holidays for Couples.
Jeffrey O'Rourke, chief executive of Ink Publishing, which confirmed it had won the contract last week, said yeahbaby would reach an affluent audience, including many frequent flyers with a second home overseas.
He added: "Each issue needed to deliver more value to the advertisers, and 10 times a year was simply too frequent for the number of travellers bmibaby has."
The magazine was launched by PSP Communications in December 2003 and Rare Publishing held the licence from January 2005.
Ink, which also publishes EasyJet's Inflight, Jet2.com's JetAway and MyTravel's Recline, will hold the licence for at least three years.
Yeahbaby will carry original content, all of which will be accessible online at a site that links to bmibaby's booking site (www.bmibaby.com), where customers make over 90% of their bookings.