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Ink, the publisher of more than 30 airline titles, has been looking to expand its portfolio of retail publications.
Ultramarine stopped trading last month.
Jeffrey O'Rourke, chief executive of Ink, said: "Over the course of the past year, we have been building up our presence in the in-flight retail market. Acquiring ARC and ARN is a big step and evidence of our commitment to the market."
ARC, which was set up three years ago, is an annual event that debates the future of in-flight retail.
ARN is a digital publication that was launched in April to promote ARC and features interviews with Andy Harrison, the chief executive of easyJet, and Tim Jeans, managing director of Monarch Airlines.
Max Williams, the founder of ARC, will stay with the business, whose airline clients include Thomas Cook, bmi, Ryanair and easyJet.