The station's long-running Midweek programme, fronted by Libby Purves, has been cancelled as a result of the changes.
The presenter will instead host a new monthly theatre show.
Purves said the new programme would "cover more fully the remarkable variety and adventurousness of British theatre around the country".
The 30-minute episodes will be broadcast once a month on a Saturday followed by a repeat during the week.
Radio 4 said Midweek would be replaced by a new interview series which would see prominent figures from the arts world interviewing each other.
The series will work as a chain - with each interviewee becoming the interviewer of a new guest on the following episode.
Four series have been commissioned by the station, with the six episodes in each series being broadcast in Midweek's former slot - 09:00 on Wednesdays.
Purves has presented Midweek since 1983 - the year after the show launched.
Radio 4 controller Gwyneth Williams described Purves as a "formidable broadcaster" and praised her for doing an "outstanding job" of presenting Midweek.
She added: "I want to thank all the guests and excellent producers who have brought such a degree of surprise and pleasure to our Wednesday mornings."
Radio 4's other weekly magazine and conversation programmes, such as Saturday Live, Loose Ends, Start the Week and Woman's Hour, are unaffected by the schedule changes.
It has also been confirmed that a broadcast of Glenda Jackson's Old Vic production of King Lear that had been part of Radio 4's Boxing Day schedule will no longer be transmitted.
A spokeswoman for the station said: "Every now and then we have to make changes to our scheduling.
"We were looking forward to bringing King Lear to Radio 4 audiences this Boxing Day, but unfortunately on this occasion we were not able to progress with this production as planned."
A documentary about the production is still scheduled to air on Christmas Day.
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BBC Radio 4 is to air two new arts programmes as part of changes to its schedule.