The media infrastructure company picked up the 63% share Global inherited when it bought GCap Media last year.
It will also take control of Now Digital, the company that runs the radio group’s local digital radio multiplexes.
Tom Bennie, chief executive of Arqiva, says the purchase will help it “invigorate DAB with new channels and services”.
“We believe in the long-term future of DAB, and this deal with Global Radio extends both of our companies’ commitments to digital radio,” he says.
DAB has been the subject of considerable debate in the last two years with many observers questioning the benefits of and radio groups’ appetite for the technology despite rising set sales and listeners.
Radio operators have also been reluctant to launch digital-only stations with only a handful currently operating.
In June, the Digital Britain report tried to address some of the issues by setting a date, 2015, for the intended upgrade of all national radio stations from analogue to digital in a bid to give reluctant operators certainty.
The report also recommended that all new car radios sold in the UK should be digital by the end of 2013.
Earlier this year, The BBC and the commercial radio sector formed a new partnership called The Radio Council designed to try to secure radio’s place in the digital age.
Separately, reports say Arqiva is currently negotiating to buy the technology developed for proposed video on demand service, Project Kangaroo.
The joint venture between ITV, BBC Worldwide and Channel 4 was blocked by the Competition Commission earlier this year.