This work was first performed in 1793 and likely dates to that year or the previous one. It was originally designed to serve as the finale to the 1801 Piano Concerto No. 2, but was discarded and not published until 1829, two years after Beethoven's death. The composer thus suppressed the Rondo in B flat throughout his lifetime, but a performing version was fashioned by Carl Czerny because some of the solo part was apparently missing or left incomplete in the surviving manuscript.

The Rondo opens with a lively, playful theme in the piano's upper register. The orchestra then immediately introduces the second subject, as well as new material. The piano is not idle for long, however, and the soloist and orchestra share many colorful exchanges. When the main theme reappears it is given more attention, this time the orchestra taking it up. Yet it is hardly dominant, allowing the equally charming and graceful secondary material to share center stage. At the center of this Rondo, Beethoven introduces a lovely, rather carefree melody—really, a variant of the main theme—whose slower pacing provides deft contrast to the livelier music surrounding it. There is a brief but brilliant cadenza near the end, after which the main theme and related materials return for a joyous conclusion.

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