Danny Baker has said he wants to "formally apologise for the outrage I caused" following "one of the worst days of my life".
He said he was "not feeling sorry for myself".
Baker tweeted: "Following one of the worst days of my life I just want to formally apologise for the outrage I caused and explain how I got myself into this mess.
"In attempting to lampoon privilege and the news cycle I went to a file of goofy pictures and saw the chimp dressed as a Lord and thought, 'That's the one!'
"Had I kept searching I might have chosen General Tom Thumb or even a baby in a crown. But I didn't. God knows I wish had.
"Minutes later I was alerted by followers that this royal baby was of course mixed race and waves of panic and revulsion washed over me.
"F**k, what had I done? I needed no lessons on the centuries slurs equating simians and people of colour. Racism at it's basest.
"I am aware black people do not need a white man to tell them this. Deleting it immediately and apologising for the awful gaffe I even foolishly tried to make light of it. (My situation that is, not the racism involved.) Too late and here I am.
"I would like once and for all to apologise to every single person who, quite naturally, took the awful connection at face value. I understand that and all of the clamour and opprobrium I have faced since. I am not feeling sorry for myself. I f****d up. Badly.
"But it was a genuine, naive and catastrophic mistake. ...
"I am now paying the price for this crass and regrettable blunder and rightly so. Probably even this final word from me will extend the mania. ('Dog whistle' anyone?) I would like to thank friends on here for their kinder words and once again - I am so, so sorry."
On Thursday, Baker, 61, insisted he was no "downbeat racist wretch" after he was sacked for what his bosses said was a "serious error of judgment".
He blasted his bosses for their handling of the controversy and said he was trying to make a point about class.
The DJ, who has been sacked from the station before, had tweeted a black and white image showing a well-dressed man and woman holding hands with a suited chimpanzee, which he captioned: "Royal baby leaves hospital."
The tweet came on the same day Harry and Meghan, whose mother is African American, posed with their new arrival, Archie Harrison Mountbatten-Windsor.
Following a backlash and accusations of racism, he deleted the post and apologised.
But, speaking to journalists outside his London home, he said it was "weasely for the BBC to chuck us under the bus".
He revealed that he ended his "lecture" from his bosses "with two very old fashioned Anglo-Saxon words".
Baker alerted fans to his sacking when he tweeted "just got fired from BBC 5 Live", before the BBC had made a statement.
BBC Radio 5 Live previously dropped Baker's soccer phone-in show in 1997 when the broadcaster's news chief Tony Hall, now the corporation's director general, said he had crossed "the line between being humorous and controversial and being insulting".
His BBC London 94.9 show was also axed in 2012, days before he was due to be inducted into the Radio Academy Hall of Fame.
The DJ has been unafraid to publicly criticise his BBC bosses, calling them "pinheaded weasels".
Baker, who hosted a weekly show on 5 Live, made his name as a journalist on the punk fanzine Sniffin' Glue before going on to work at NME and launching a career in TV and radio.
He denied bullying campmates in 2016 when he was the first in the series to get the boot from I'm A Celebrity.