The work is orchestrated for solo piano, flute, two oboes, two bassoons, two horns, and strings. As is typical with concertos, it is in three movements:
- Andante in C major
- Allegretto – Presto
According to the date that the composer himself noted on the score, the concerto was completed on April 12, 1784.
The date of the premiere is uncertain. In one view, the work is said to have been premiered by Mozart's student, Barbara Ployer, on June 13, 1784 at a concert to which Mozart had invited Giovanni Paisiello to hear both her and his new compositions, including also his recently-written Quintet in E flat for Piano and Winds. Afterwards, Ployer was joined by Mozart in a performance of the Sonata for Two Pianos, K. 448. Another possibility, advanced by Lorenz (2006, 314), is that Mozart did not wait over two months to premiere the work, but performed it in his concert with Regina Strinasacchi on 29 April 1784 at the Kärntnertortheater. As a general consensus for researchers, it can be said with relative certainty that the work premiered during the mid-to-late spring of 1784, following its completion.