Green, 56, and Cass, 60, have both been familiar fixtures on Radio 4 since the 1970s, introducing programmes, reading news bulletins for the Today programme, or delivering the Shipping Forecast.
However, they will leave the station in the new year as the BBC cuts its announcing team down from 12 to 10.
Speaking to The Daily Telegraph, Radio 4 controller Gwyneth Williams said: "Harriet Cass and Charlotte Green have made an immense contribution to Radio 4. We will all miss them - and I know I speak for listeners as well as colleagues.
"They have both chosen to move on and they go with my personal respect and affection as well as the good wishes of everyone who has grown to know and love them over many years."
Green, who joined the BBC in 1978 as a studio manager and was once named 'Most Attractive Female Voice on the Radio' in a Radio Times poll, said that she had "thoroughly enjoyed" working for the corporation over the last 34 years.
"I'll miss the buzz of live radio, but I'm really looking forward to getting involved in new projects."
After joining the BBC in 1972, Cass worked as a reporter from Westminster and produced Today in Parliament, before being promoted to a senior announcer.
Yesterday, she said: "The BBC was my first job and I thought it would be interesting for a few months. Forty years later, it's time to do other things.
"It has been a real privilege to have been part of the Radio 4 family for so long. It has also been a lot of fun."
The departure of Cass leaves Chris Aldridge as Radio 4's most senior announcer.