It was commissioned by William Primrose, a respected violist who knew that Bartók could provide a challenging piece for him to perform.

[1] Bartók was suffering the terminal stages of leukemia when he began writing the piece and left only sketches at the time of his death.

The concerto was premiered on December 2, 1949, by Primrose and the Minneapolis Symphony Orchestra, with Antal Doráti conducting.

[8] Bartók's manuscript only specifies flute, oboe, 2 clarinets, bassoon, horns, 2 trumpets, timpani, strings.

Serly's edition is orchestrated for piccolo, 2 flutes, 2 oboes, 2 clarinets in B♭, 2 bassoons, 3 horns in F, 3 trumpets in B♭, 2 trombones, tuba, timpani, percussion and strings.

Peter Bartók and Paul Neubauer's edition is orchestrated for piccolo, 2 flutes, 2 oboes (2nd doubling cor anglais), 2 clarinets in B♭, 2 bassoons (2nd doubling contrabassoon), 4 horns in F, 3 trumpets in B♭, tenor trombone, bass trombone, tuba, timpani, percussion (2), strings.

Some editions contain more changes than editor markings; in Peter Bartók's revision, measures are added, completely missing, or with note changes.

This trend of alterations continues as Peter Bartók adds octave displacements, and omits what is measure 74 in Serly's version.

After the completion, a gathering of friends of Bartók expressed an eight-to-six preference for the cello transcription over the original.