The deal is subject to clearance by QMS shareholders and foreign investment regulators in Australia and New Zealand, the company added.
QMS operates across Australia, New Zealand and Indonesia specialising in digital and static billboards, street furniture, and sport, airport and transit media.
Last year the company completed the acquisition of 40 per cent of MediaWorks via a merger of its New Zealand subsidiary. The remaining 60 per cent of MediaWorks is owned by New York hedge fund Oaktree Capital.
Oaktree became a shareholder of MediaWorks in 2015 when it bought the minority shareholdings of rival private equity firms TPG Capital and Bain Capital, following receivership and a debt restructure.
Last week MediaWorks revealed plans to sell its TV business and its Auckland headquarters amid ongoing challenges in the media business.
Chief executive Michael Anderson dismissed any suggestion that the announcement was an attempt to force the Government's hand over regulations governing TVNZ.