Streisand was left open-mouthed as her former co-star appeared from behind the scenes during her appearance on Oprah Winfrey's US chat show.
The couple shared a tender hug before sitting down together for the first time in 37 years.
Asked why they had never been interviewed together before, Redford joked: 'Because I thought I wouldn't get a word in.'
Streisand and Redford played star-crossed lovers Katie Morosky and Hubbell Gardiner in 1973 box office hit The Way We Were.
The movie even earned Streisand a Best Actress Oscar nomination and won the Academy Awards for Best Original Score and Best Original Song.
The singer's on-screen reunion with Redford marks yet another scoop for the final season of the Oprah Winfrey Show.
Within the last fortnight the chat show host has aired sought-after interviews with Michael Jackson's parents, Marie Osmond and Ricky Martin.
Oprah's interview with Streisand and Redford airs in the United States today.