A total of 51.9 million people watched at least 15 minutes of the London games on BBC TV, which offered blanket coverage of the Olympics on BBC1 and BBC3 and 24 dedicated Olympics channels on satellite, cable and online.
The corporation said 24.2 million people (42% of the UK population) watched at least 15 minutes of the games via the BBC red button.
The top 10 Olympics events all had peak audiences of more than 12 million viewers.
Cohen said: "The fact that Team GB did so well created a huge public interest and momentum.
"It's been a real breakthrough moment for the BBC in terms of digital and our relationship with audiences in a digital environment.
"I doubt there has been a sustained period since the mid-1990s when we have had such consistently large audiences, the largest since the pre-digital age."
Initial BBC figures suggested the closing ceremony, which had an average audience of 23.2 million viewers, was watched by even more people than Danny Boyle's opening ceremony, which had an original overnight rating of just over 23 million.
But on Monday, the day after the games finished, the corporation gave a belated boost to the audience for Boyle's opening spectacular, and said it was actually watched by an average of 23.4 million viewers when viewing on digital channels and BBC News was taken into account. The BBC also upped its peak audience from 26.9 million to 27.3 million.
The BBC said the London Games was the "biggest national television event" since current Barb methodology was introduced in 2002.
Reaching 90% of the population, it eclipsed the 81% of the population who watched at least 15 minutes of the 2002 football World Cup, the 69% who watched the BBC's coverage of the Queen's diamond jubilee earlier this year and the 61% who saw last year's royal wedding."