Jan Boehmermann, host of satirical programme "Neo Magazin Royale" on public broadcaster ZDF, said he had been waiting since Sunday for someone to ask him if he had faked the controversial footage, but no one had questioned him.
"Sorry Mr Varoufakis, we won't do it again," he said, detailing how a production team had manipulated the video.
The footage showed Varoufakis before he became finance minister speaking at a 2013 event in the Croatian capital of Zagreb.
In the doctored images Varoufakis talks about the problems facing his debt-laden country, and says "stick the finger to Germany" as he makes the offensive gesture.
Greece and Germany, Europe's paymaster, have been at loggerheads since Greece's radical-left Syriza party came to power in January on promises of ending austerity and erasing most of the country's massive debt.
The footage, originally shown during the Guenther Jauch weekly talk show on Germany's ARD channel late on Sunday, prompted an immediate and vehement rebuttal by the maverick Greek minister, who was a guest on the programme.
Varoufakis, who took part in a live discussion with other guests via a link from Athens, insisted on air that the video had been "doctored".
Jauch's show, which draws millions of viewers, said Monday it had seen "no indication whatsoever of manipulation or falsification in the video shown during the live show".
It said the video was being further checked by experts.
However Boehmermann said Wednesday his team had doctored the footage in late February, and described manipulating shadows to make the changes more realistic.
ZDF did not confirm his statement but retweeted a link to his confession.