The 79-year-old made the claim while she collected the Outstanding Achievement Award during the TRIC Christmas Lunch on Tuesday in London.
During her acceptance speech, the Strictly Come Dancing alum told the audience she was urged to resign by Birt aged 50 because she'd “had her day”.
She began: 'It's actually now 57 years since I've started doing broadcasting. When I was 50, I had a conversation with the then director general of the BBC, who was called John Birt, who said I was having a bit of a problem with something at the BBC.
“He said to me, ‘Angela, you have to recognise now that you're 50, you've had your day and it's time to make way for the younger women coming up behind you.’
“So he managed to be a misogynist and an ageist in one statement, which I thought was quite a trick, and the thing is, John Birt, you said I've had my day, [but] what I've actually had right up until now, is the time of my life.”
Rippon, who became the first woman to front the news in 1974, went on to share how “extremely proud” she is of the women who are now reading the national news.
She continued: “When he said I had to make my way for younger women coming up behind me, I have to say one of the great pleasures of my half a century now in broadcasting - I am a little bit older than commercial radio.
“In that half century, it has been wonderful for me, having been something of a novelty when I started to read the news for the first time on national television, as the only woman who was reading it nationally.
“To find so many wonderful, young women have climbed up through that hole in the glass ceiling behind me. I am so proud of every one of them, all of those women of all ages now who have demonstrated by their skill and by talent - they're not fulfilling an HR box ticking exercise.
“They're there on merit because what they do, and they stand shoulder to shoulder with their male colleagues. And there is respect on both sides, and I love that now about the industry in which I work.”
The TV star, who began her career in 1966 aged 21, concluded her speech by saying: “And one final message to John Birt, when I was 50, you said I'd had my day. I'm now 79, and I ain't finished yet!”
The Standard has contacted a BBC spokesperson for comment.