Russell Brand has resigned from his Radio 2 programme following prank calls he made with Jonathan Ross to actor Andrew Sachs.
It follows a public apology from Ross over his "juvenile and thoughtless remarks" in the calls.
Earlier, it was announced the pair would be suspended and all their shows taken off air until the BBC has investigated the calls made on Radio 2.
Fawlty Towers actor Sachs, 78, said he had "respect" for Brand's decision.
Sachs was upset after Brand and Ross left a series of lewd messages on his voicemail as part of a pre-recorded show, taped on 16 October.
The pair made obscene comments about the actor's 23-year-old granddaughter Georgina Baillie during four separate phone calls.
Brand said in a statement that he took "complete responsibility" for the incident.
"As I only do the radio show to make people laugh I've decided that, given the subsequent coverage, I will stop doing the show," he said.
He added: "I got a bit caught up in the moment and forgot that, at the core of the rude comments and silly songs, were the real feelings of a beloved and brilliant comic actor and a very sweet and big-hearted young woman."
Earlier, he told reporters waiting outside his home: "I'm sorry that I have upset Mr Sachs."
He had presented his Saturday night show since November 2006 and is believed to have been paid more than £200,000 a year.
I am not going to take it anywhere. I'm not out for revenge
Meanwhile, Ross said in his statement: "I am deeply sorry and greatly regret the upset and distress that my juvenile and thoughtless remarks on the Russell Brand show have caused."
He said he had not issued a statement before because he had intended to apologise "to all those offended" on his Friday night chat show.
"However, it was a stupid error of judgement on my part and I offer a full apology," it added.
During the calls, Ross swore and said Brand had slept with Sachs' granddaughter.
Brand and Ross are my two favourite BBC entertainers. They provide me with laugh out loud moments!
More than 27,000 people have complained to the BBC while watchdog Ofcom has launched its own investigation.
The corporation's governing body, the BBC Trust, has called a special meeting of its editorial standards committee for Thursday.
Director general Mark Thompson will report management findings to the meeting and tell bosses what action he plans to take.
'Breach of privacy'
Announcing the suspensions in an earlier statement, Mr Thompson said he would be returning from a holiday and would "in the coming days, announce what action we will take".
This gross lapse of taste by the performers and the production team has angered licence payers
"Since Sunday, I have been in regular contact with the senior executives I tasked with handling this issue," he said.
"In the meantime, I have decided that it is not appropriate for either Russell Brand or Jonathan Ross to continue broadcasting on the BBC until I have seen the full report of the actions of all concerned.
"This gross lapse of taste by the performers and the production team has angered licence payers."
He added his "own personal and unreserved apology to Andrew Sachs, his family and to licence fee payers for the completely unacceptable broadcast".
BBC One show Friday Night with Jonathan Ross was due to have been filmed at BBC Television Centre, west London, later on Wednesday.
Guests on the show were to have been Sir David Attenborough, comedian Frank Skinner, US teen singer Miley Cyrus and band The Killers.
A decision has yet to be taken on what should be shown in its place on Friday night.
Ross's Saturday morning radio show, has also been pulled from Radio 2's schedules.
'Lovely old man'
Georgina Baillie said "justice" had been done over the suspensions
"Me and my granddad are both really happy," she added.
"I'm glad it's all over with, as far as I'm concerned."
Earlier, she told the paper: "What's funny about humiliating a lovely old man who has never harmed anyone in his life?"
Brand and Ross were "beyond contempt"," she added.
Prime Minister Gordon Brown criticised the pair for "inappropriate and unacceptable behaviour", while Conservative shadow culture secretary Jeremy Hunt said in a speech on Wednesday that it was "wrong for broadcasters to produce programmes that legitimise negative social behaviour".
He told BBC News the corporation's reaction to the affair was "concerning".