Dunne has been leader of the telecoms giant since April 2008. Prior to this he was chief financial officer and head of finance, having joined O2 before its demerger from BT in 2001.
He is also chairman of Tesco Mobile, the UK's largest mobile virtual network operator, a joint venture between Tesco and O2. During his career, he has held senior financial positions in the banking and the corporate sectors.
Amelia Fawcett, chair of GMG, said: "Ronan's experience with consumer-focused brands and his commitment to developing innovative digital products, combined with his understanding of the technology space, will be a huge asset to GMG.
Dunne said: "The media sector is changing, which presents enormous opportunity as the true potential of digital services and interaction becomes a reality."
Also joining Guardian Media Group as non-executive director is John Paton, chief executive of Digital First Media.
Digital First Media, which operates Digital First Ventures, MediaNews Group and Journal Register Company, has print and online divisions across the US, Canada and Europe.
Paton oversees the operation of more than 800 digital and print products in 18 states across the US, serving 61.5 million customers per month.
Fawcett said: "John's deep understanding of the opportunities presented by digital and his commitment to quality journalism are closely aligned with GMG's digital-first strategy, while his experience of helping legacy media companies to make the transition to successful multi-platform media companies will be invaluable as we continue to take our business forward.
"The depth and range of expertise on the GMG board means we are fully equipped to support our transformation to a digital-first organisation, strongly placed to ensure a long-term, commercially successful future for our journalism."