Ross was suspended last year for three months for taking part in a sexually charged radio prank, along with comedian Russell Brand. Ross later apologized for the incident.
Streisand is expected to perform some of her classic songs, as well as material from "Love is the Answer," her first new album since 2005, on Ross's program Oct. 2.
The special edition of the chat show "Friday Night with Jonathan Ross" will be called "Friday Night with Streisand and Ross" in her honor, the BBC said.
Streisand's publicist said this marks the singer's first studio interview in Britain since the 1980s.