QMS - which previously owned just under 55% of MediaWorks - bought the remaining 45% owned by US investment company Oaktree Capital Management.
MediaWorks owns well-known radio stations, including The Breeze, Mai FM, More FM and The Rock.
It previously owned television channel Three before it was sold to US-based Warner Bros. Discovery.
On the full QMS takeover, MediaWorks chief executive Wendy Palmer said she was "excited about this milestone".
"Since 2019, MediaWorks has built a strong relationship with QMS, and this transaction marks the next chapter in our partnership," Palmer said.
QMS and MediaWorks chairperson Barclay Nettlefold said the deal grew QMS' presence in New Zealand.
"Combined with MediaWorks' dominant position in radio and digital audio, the partnership creates a premier media platform for advertisers seeking to reach audiences across Australia and New Zealand," Nettlefold said.
The value of the deal was not disclosed, and it was subject to regulatory approvals.
