The London-based customer publisher will publish its first issue of Hemispheres, which has a print run of 350,000, in March.
The brief for Hemispheres, now in its sixteenth year of publication, was previously handled by Pace Communications.
United Airlines claims to have flown 92 million passengers last year, compared to BA which flew 33.2 million passengers.
Ink publishes 34 in-flight magazines, more it claims than any other company in the world. It has offices in New York, Hong Kong, Singapore and Atlanta, as well as London.
Jeffrey O'Rourke, chief executive of Ink Publishing, said the company aimed to make Hemispheres "the most dynamic and engaging magazine in the air".
In October, the contract magazine publisher announced it is to launch its second title in India in a month, after it secured the publishing duties for in-flight entertainment guide Air Premier for Kingfisher Airlines' international routes.