The influential policy advice vehicle, which has close links to the Conservative party, believes that the BBC should spend less money on commissioning mass-market entertainment shows and acquiring sports rights.
Published today, the thinktank's Changing The Channel report on public service broadcasting argues that Channel 4 should be put on the market. The broadcaster is currently owned by the government but funded by commercial activities.
The report further calls for the BBC Trust to be abolished as it has failed to bring BBC management to account. The body would instead be replaced by a Public Service Content (PSC) Trust to oversee all PSB material across TV, radio and online platforms.
As public broadcasters are currently under severe strain, Policy Exchange believes that a radical overhaul is required to help the sector prosper in the digital age.
The thinktank argues that increased competition means that the main channels are being held back by their PSB obligations, in which terrestrial licenses are awarded in exchange for producing certain types of programming.
As a remedy, the report calls for ITV, Channel 4 and Five to be allowed to opt out of their PSB status by the end of the digital switchover in 2012. However, Channel 4 must retain its public obligations for at least ten years.
Channel 4, which is valued at around £500m, would keep the "majority" of proceeds from its sale in order to improve its beleaguered balance sheet. Privatisation could also usher in a long-mooted merger with Five to create a highly competitive commercial broadcaster.
Under the Policy Exchange approach, a privatised Channel 4 would be regulated by the new PSC Trust to ensure that it upheld its PSB obligations.
The BBC Executive would also report to the PSC Trust, but a new BBC joint board would bring the corporation's management to account on a day-to-day basis. Ofcom would retain its role of regulating broadcast content, including all matters of taste and decency.
Report author Mark Oliver, a former head of strategy at the BBC, said that current arrangements for UK public broadcasting are starting to show their age.
"The current UK broadcasting system was set up in the 1950s and now struggles to keep up with the extraordinary changes of the digital age," he said.
"It is clear that the 20th Century analogue institutions that were created are now worryingly out of date. We need a dramatic rethink if we are to continue to deliver public service broadcasting in an entirely new age."
Policy Exchange further wants wider use of the £3.7bn annual licence fee to fund PSB programming beyond the BBC, in a process it calls "bottom slicing".
Under the approach, rival broadcasters would be able to tender for a portion of public money for making specific types of content. By 2018, the BBC would be required to allocate 5% of the licence fee for "third party services and programming".
The approach would be particularly useful for reaching the 16 to 35-year-old audience, with around £30m potentially being diverted to fund Channel 4 or E4 content rather than £100m spent on BBC Three.
Channel 4 would also receive additional digital capacity from the BBC and ITV, along with access to the BBC's new media services, including BBC iPlayer.
Responding to the report, a BBC Trust spokesman said: "For its part, the Trust has been focused on protecting the public value and independence of the BBC against inappropriate political or commercial influence.
"Anyone proposing change to the current governance arrangements must demonstrate that they won't put either that value or that independence at risk. In the meantime we are getting on with the day job of getting the best out of BBC for licence fee payers."
A Channel 4 spokesman welcomed the report's positioning of Channel 4 as a "key source of public service competition to the BBC", but also opposed calls for privatisation.
Speaking to The Guardian, he said that the broadcaster remains "firmly of the view that our publicly owned, not-for-profit status is the most effective means of ensuring that Channel 4 can continue to play the public service role that the report so strongly endorses".