The presenters took to Twitter to apologise, telling followers they had "stopped" the stretches several years ago amidst racism controversy.
In the statement, Ant and Dec wrote: "During past episodes of Saturday Night Takeaway we impersonated people of colour in the undercover segment of the show.
"We realise this was wrong and want to say that we are sincerely sorry to everyone that was offended.
During past episodes of Saturday Night Takeaway we impersonated people of colour.
"We purposely stopped doing this several years ago and certainly would not make these sketches today.
"We had already taken steps to ensure footage was taken down and have again recently confirmed with ITV that these segments, and any other historical content, that could cause offence, does not appear on either the ITV Hub or the Saturday Night Takeaway YouTube channel."
The famous pair, both 44, often wear prosthetics and disguises to trick celebrities on the ITV show.
They previously appeared as Jamaican women Patty and Bernice as extras on the set of Emmerdale on the series in 2003.
The footage seemingly resurfaced last year, alongside an old interview in which the pair joked about the characters.
In the clip taken from their Saturday Night Takeaway DVD, Ant said: "It was funny sitting in a room, learning Jamaican, picking dresses, trying on false nails, was something I didn't think I'd ever, ever do."
Dec added: "We had to find who Patty and Bernice were, so we'd have to go 'Well, I think Bernice probably came to England on a boat'."
Their statement comes days after comedy show Little Britain was removed from Netflix and BBC iPlayer in light of recent Black Lives Matter protests around the world.
The series starred Matt Lucas and David Walliams and featured some episodes where the actors don blackface.
A spokesman for the BBC told MailOnline: "There's a lot of historical programming available on BBC iPlayer, which we regularly review.
"Times have changed since Little Britain first aired so it is not currently available on BBC iPlayer."
Streaming service BritBox has also removed the show, along with Walliams and Lucas' other programme Come Fly With Me.
A spokesperson for BritBox explained: "Times have changed since Little Britain first aired. So it is not currently available on BritBox.
"Come Fly With Me has not been available on the service for six months."
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