He replaces Jason Cotterrell who moves to the newly created role of group development director at the out-of-home company.
Exterion Media has boosted its position in the UK after Cotterrell helped to win Transport for London’s expanded, eight-year £2bn outdoor contract last year.
King said he was ambitious for the business, which competes with bigger international rivals JCDecaux and Clear Channel.
"We have the opportunity to take this company to market leadership, through greater investment in digital and through the right culture and people," King said. "I believe we can digitise our business model faster than any of our competitors."
Shaun Gregory, the chief executive of Exterion Media, who used to work with King at Emap, said overtaking JCDecaux to become number one in the UK was a key aim.
"We're number two, we're clearly the challenger brand in the UK," Gregory said, describing the appointment of King as "a very clear statement of intent".
King will start on 23 January with little experience of out-of-home but said: "OOH has proved itself over and over again. It’s remained resilient in tough times, and delivered market-beating growth in the good times."
Before TMG, King was managing director of advertising at Emap, the magazine and radio group, where he spent six years from 1999 to 2005. Gregory and King did not work closely together at Emap.
Gregory said: "Attracting someone of Dave’s calibre speaks volumes about our business. He has a first-class track record across all forms of media, and the necessary experience in transitioning traditional business models into the digitised world we live in today."
He added that King had proved himself by developing "new revenue streams" during his 12-year stint at TMG, knows "both the buy and sell side of our sector" after previously working as head of investment at Carat, and is "clearly well suited to the world of private equity".
Platinum Equity owns Exterion Media, which describes itself as "Europe’s largest privately owned OOH company".
Campaign reported last year that Platinum was considering a £1bn stock market flotation for Exterion Media, but it put the idea on hold after the Brexit vote.
Gregory, who also came to Exterion Media with little experience of outdoor, has been keen to reposition the business as a digital media company, driven by data, rather than just an out-of-home company.
"Dave is joining the business at a pivotal time as we embark on the next chapter of our journey," Gregory said, explaining it was important to bring in an outsider.
There has been speculation for some time that King was to depart as executive director of TMG as it has made a string of senior commercial hires, including Robert Ffitch as director of advertising revenues and Nick Hugh as chief operating officer.
Murdoch MacLennan, chief executive of TMG, praised King’s "fantastic contribution" since 2005 in "transforming" the print publisher into "an industry-leading media group".
King has most recently been working for TMG on plans to set up a joint ad sales operation with rival publishers to stem falling revenues and did a course at Harvard Business School.
He "leaves us in a strong position to deal with the challenges we face", according to MacLennan.
Cotterrell will focus on "future growth", including franchise opportunities, partnerships and new technologies in both the UK and other markets.
He has worked for over 20 years at Exterion Media, including as UK managing director since 2011.
Cotterrell said he was "immensely proud" of Exterion’s "significant growth" during his time in charge, describing the TfL win as the highlight of his time in charge.
"I believe we’re in a hugely exciting phase of growth – not just for our business, but for the wider industry," he said.
Cotterrell begins his new role in March, after a handover with King, and will report to the group chief operating officer, Leon Taviansky.