In his first major confrontation with the corporation since becoming prime minister, Johnson lashed out at its decision to scrap the free licence for all but the poorest pensioners over 75 from next year.
Up to 3.7m pensioners will have to start paying £154.50 a year from next June, with only households on pension credit benefit remaining exempt.
The BBC, which blames the move on the government’s squeeze on its own budget, will collect around £745m from 2021, rising to more than £1bn by 2029, from charging older viewers.
Speaking to reporters at the G7 summit, Johnson was asked if the Tories would honour their 2017 manifesto pledge to protect pensioners’ benefits from TV licences to winter fuel.
He replied: “The BBC received a settlement that was conditional upon their paying for TV licences for the over-75s. They should cough up.”
The BBC has argued that it has been forced to charge older viewers and listeners because of the squeeze imposed on its finances by David Cameron’s government.
A BBC spokesperson said: “It was the government who decided to stop funding free TV licences for the over 75s, and parliament gave responsibility to the BBC to make a decision on the future of the scheme.
“There was no guarantee that the BBC would continue to fund free licences for the over 75s, as the culture secretary at the time has confirmed.
“We’ve reached the fairest decision we can in funding free TV licences for the poorest pensioners, while protecting BBC services.
“If the BBC funded all TV licences for the over 75s it would mean the closure of BBC Two, BBC Four, the BBC News Channel, the BBC Scotland channel, Radio 5 Live, and several local radio stations. It is a matter for the government if it wishes to restore funding for free licences for all over 75s.”
Johnson was embroiled in another spat with a broadcaster on Sunday after he pulled out of a planned interview with Channel 4 News in an apparent retaliation for its news chief comparing him to Vladimir Putin.
The BBC’s director-general, Lord Hall, has said its agreement with the corporation was taken four years ago shortly after Cameron’s election victory.
“Remember the context of this - 2015, height of austerity, incoming Conservative Government,” Lord Hall told a Lords committee in June.
Philippa Childs, head of the broadcasting union Bectu, said: “It’s very disappointing that Boris Johnson continues with the narrative that the BBC knew what they were taking on.
“The reality is that they were given little or no choice at the time, when austerity was at its peak and ministers were looking for a convenient way to pass the buck on taking difficult decisions about welfare payments.”
Labour’s deputy leader and shadow culture secretary, Tom Watson, said: “This prime minister’s disregard for older people is appalling. He is trying to blame the BBC for his own government’s policy, but this obfuscation will not work.
“This government must stop passing the buck and step in to fund the free TV licences today.”
But James Roberts, political director of the TaxPayers’ Alliance, said: “After the kickback against dragging pensioners into paying the dreaded TV tax, the PM is tuning into the public mood.
“The Beeb should be moving towards a funding model where subscription fees replace part or all of the license fee, so that we can just axe the TV tax and only those who watch it need to pay.”