In the Disney movie Beauty and the Beast, this is sung by Kathryn Flynn as Mrs. Potts the teapot. The single release version is by Celine Dion and Peabo Bryson. Both this and "A Whole New World (Aladdin's Theme)" were sung by Peabo Bryson and won Academy Awards for Best Song. Two other songs from the movie - oddly enough also starting with "B" - were also nominated for Best Song: "Belle" and "Be Our Guest."
Along with the other songs in the movie, this was written by Alan Menken and Howard Ashman, who had scored The Little Mermaid. Sadly, Ashman's life was cut short by AIDS shortly before the film came out and he never lived to see its victory for Best Song.
The message of the song is that a couple can be "as old as time" no matter how different they are. Among those who have covered it are Steve Tyrell and Kenny Loggins. In 1994 Beauty And The Beast became the first Disney film to make it to Broadway.
This was Celine Dion's first UK single. She had already scored in America with "Where Does My Heart Beat Now" and "(If There Was) Any Other Way."
Suggestion credit: Sara - Silver Spring, MD, for all above
John Legend and Ariana Grande covered this for the soundtrack of Disney's 2017 live-action adaptation of Beauty and the Beast.