Of American-English origin, the noun jukebox denotes a machine—typically a large brightly lit glass-fronted cabinet—which automatically plays a selected musical recording when a coin is inserted.

In jukebox, the noun juke denotes a cheap roadside establishment providing food and drinks, and music for dancing.

An earlier Floridian appellation was jook organ, also juke organ. The earliest occurrence of this that I have found is from the column Law and Disorder, by Kenneth Ballinger, staff writer for The Miami Herald (Miami, Florida, USA), published in that newspaper on Friday 7^th May 1937:

More authorities on the current pastime of juking are springing up. The Tallahassee Lions’ club in their weekly bulletin report that their editor favors the spelling “jooking” and declare further that nickel-in-the-slot machines, particularly the music boxes found in these night spots, are being called jook organs.
Carl Hanton of The Fort Myers News-Press in a recently scholarly discussion of the subject stated that the pronunciation of the word juke should rhyme with took, but this has unfortunate connotations that make it unwise to pursue the subject further. He and the other modern writers are agreed, however, that the spelling should be juke instead of jook, as favored by the Tallahassee Lions.
We give you, therefore, the appellation of juke organ as indicating any one of that numerous family of alleged musical and amusement devices which have their finest appeal in the oftimes [sic] maudlin atmosphere of the contemporary night spots.

The following definition is from A Note on Jook, by Will McGuire, Editor of The Florida Review, the official student publication of the University of Florida (Gainesville, Florida, USA), published in the Spring 1938 issue of that magazine:

Jook-organ: the nickelodeon, or coin phonograph playing a choice of a dozen or so records, found invariably in a jook. In central Florida a coin phonograph is called a jook-organ now, whether or not its is found in a jook.

The earliest occurrences of the noun jukebox that I have found are as follows, in chronological order:

1-: From Phonograph Boom, published in Time (New York City, New York, USA) of Monday 4^th September 1939:

Seven years ago the U. S. phonograph and record industry was so sick its own backers almost gave it up for dead. Today, it is not only up and around again; it has fattened into one of the fastest growing businesses in the U. S., with an annual gross of some $36,000,000. […]
[…]
Once the upswing had its initial bounce, other factors kept it moving. Most important of these was the popularity of the slot machine or “juke box” which retailed melody in small barrooms, lunch-counters and dance joints at 5¢ a shot. With an estimated consumption rate of more than 30,000,000 discs annually, the 300,000 juke boxes in the U. S. are today the record industry’s largest customer.

2-: From the column Post Scripts, by Charles F. Davis, published in the Monrovia Daily News-Post (Monrovia, California, USA) of Tuesday 12^th September 1939:

CIRCULATION
Lawrence E. Jones, who operates the Jones Malt Shop on West Foothill, marked 20 nickles the other day with a dab of red nail polish, as a means of identification for use in the automatic phonograph, better known as the juke box. These nickels got back into his till, of course and were passed out from time to time in change. Interested to see if money really does circulate, as he had been told, Proprietor Jones kept an eye on his red-tabbed coins, and found that they keep turning up at his place of business, two or three a week. If you find one, drop in and spend it with him. See if he spots it.

3-: From the column Springfield Slants, by Allen Oliver, published in the Springfield Leader and Press (Springfield, Missouri, USA) of Tuesday 10^th October 1939:

Among song writers and other musicians, nickel phonographs are known as “juke boxes.” We don’t know why. Or juke care?

4-: From News Nuggets, published in the Buffalo Evening News (Buffalo, New York, USA) of Tuesday 10^th October 1939:

Swing addicts call coin phonograph machines “juke boxes.”

In 1939, jukeboxes contributed to the commercial success of the U.S. big-band leader, arranger, composer and trombonist Alton Glenn Miller (born 1904-disappeared 1944)—as mentioned in the following two articles:

1-: New King, published in Time (New York City, New York, USA) of Monday 27^th November 1939:

At first Miller’s was rated as just another good swing band. But last summer, when it moved to Westchester’s Glen Island Casino, things began to happen. Within five months Glenn Miller’s band was causing more rug-dust to fly, making more phonograph records, and playing more radio dates than Goodman and Shaw together. Last month the Chesterfield Hour conferred swing’s Pulitzer Prize on Miller by signing him up to take Paul Whiteman’s place, beginning Dec. 27. Last week Trombonist Miller, now undisputed King of Swing, went back to play a week’s engagement, just for old times’ sake, at the Meadowbrook Club.
Glenn Miller attributes his crescendo to the “juke box,” which retails recorded music at 5¢ a shot in bars, restaurants and small roadside dance joints, and has become the record industry’s biggest customer. Of the twelve to 24 discs in each of today’s 300,000 U. S. juke boxes, from two to six are usually Glenn Miller’s.

2-: Swing Loses Lead Among Best-Selling Records, published in Life (New York City, New York, USA) of Monday 18^th December 1939:

The phonograph-record business, continuing its phenomenal boom, is again having a great year. […] Riding the crest of this wave is a long-legged trombonist from Clarinda, Iowa, named Glenn Miller. His well-disciplined band is selling more records right now than any other jazz band in the business.
[…] His greatest success has been with “juke boxes,” the nickel-in-the-slot automatic phonographs. Miller is easily the most outstanding juke-box artist of 1939.

The noun jukebox has been borrowed into French. The earliest occurrence that I have found is from a correspondence from Hollywood, California, by Forrest J. Ackerman, published in V (Marseille, Bouches-du-Rhône, France) of Sunday 12^th May 1946—the following is about the French singer-songwriter Jean Sablon (1906-1994), who had completed a three-week contract at Ciro’s, a nightclub on Sunset Boulevard, Hollywood:

Les derniers disques qu’il a enregistrés […] seront bientôt dans tous les juke-boxes, ces phonos automatiques qu’on trouve partout aux Etats-Unis.
     translation:
The latest discs he has recorded […] will soon be in all the juke-boxes, those automatic phonos that are found everywhere in the United States.