Answer by taking a quote from the following article:

Rhapsody in Blue is a 1924 musical composition by American composer George Gershwin for solo piano and jazz band, which combines elements of classical music with jazz-influenced effects. Commissioned by bandleader Paul Whiteman, the composition was orchestrated by Ferde Grofe several times, including the original 1924 scoring, "theater orchestra" setting published in 1926, and the symphony orchestra scoring published in 1942, though completed earlier. The piece received its premiere in the concert, An Experiment in Modern Music, which was held on February 12, 1924, in Aeolian Hall, New York, by Whiteman and his band with Gershwin playing the piano. The editors of the Cambridge Music Handbooks opined that "The Rhapsody in Blue (1924) established Gershwin's reputation as a serious composer and has since become one of the most popular of all American concert works."

Two audio recordings exist of Gershwin performing an abridged version of the work with Whiteman's orchestra: an acoustic recording made for Victor on June 10, 1924, and running 8'59'' (this recording includes the original clarinetist, Ross Gorman, playing the glissando) and a Victor electrical recording made April 21, 1927, running 9'01'' (about half the length of the complete work). This 1927 version was also dubbed onto an RCA Victor  33 1/3 rpm Program Transcription in 1932. The latter version was actually conducted by Nathaniel Shilkret after an argument between Gershwin and Whiteman. A 1925 piano roll captured Gershwin's performance in a two piano version. Whiteman's orchestra also performed a shortened version of the piece in the 1930 film The King of Jazz featuring Roy Bargy on piano. Whiteman re-recorded the piece on both sides of a 12-inch Decca 78 rpm (29051) recorded on October 23, 1938. The first complete recording, with pianist Jesus Maria Sanroma and Arthur Fiedler conducting the Boston Pops Orchestra, was issued by RCA Victor in 1935.  Since the mid-20th century, the 1942 version has usually been performed by classical orchestras playing the expanded arrangement. In this form, it has become a staple of the concert repertoire. It has direct popular appeal while also being regarded respectfully by classical musicians.  On August 21, 1945, a recording by Oscar Levant with the Philadelphia Orchestra (conducted by Eugene Ormandy) entered at its peak position of number 23 on the Cash Box survey (Columbia Masterworks 251).  In 1973, the piece was recorded by jazz-rock artist Eumir Deodato on his album Deodato 2. The single reached Billboard peak positions number 41 Pop, number 10 Easy Listening. A disco arrangement was recorded by French pianist Richard Clayderman in 1978 and is one of his signature pieces.  In the late 1970s, interest in the original arrangement was revived. On February 14, 1973, it received its first performance since the 1920s: Kenneth Kiesler secured needed permissions and led with work with pianist Paul Verrette on his U. of New Hampshire campus. Reconstructions of it have been recorded by Michael Tilson Thomas and the Columbia Jazz Band in 1976, and by Maurice Peress with Ivan Davis on piano as part of a 60th-anniversary reconstruction of the entire 1924 concert. Andre Watts (1976), Marco Fumo (1974), and Sara Davis Buechner (2005) released recordings of the work for solo piano as did Eric Himy (2004) in a version that featured the uncut original short score. Meanwhile, such two-piano teams as Jose Iturbi and Amparo Iturbi, France Veri and Michael Jamanis and Katia and Marielle Labeque, also recorded the piece. Michel Camilo recorded the piece in 2006, winning a Latin Grammy award.

Who put together the orchestration
Two audio recordings exist of Gershwin performing an abridged version of the work with Whiteman's orchestra: