Romberg was born in Hungary as Siegmund Rosenberg to a Jewish family, Adam and Clara Rosenberg, in Gross-Kanizsa (Hungarian: Nagykanizsa) during the Austro-Hungarian kaiserlich und königlich (Imperial and Royal) monarchy period. In 1889 Romberg and his family moved to Belišće, which was then in Hungary, where he attended a primary school. Influenced by his father, Romberg learned to play the violin at six, and piano at eight years of age. He enrolled at Osijek gymnasium in 1897, where he was a member of the high school orchestra. He went to Vienna to study engineering, but he also took composition lessons while living there. In June 1909, he boarded the SS Oceanic as a second-class cabin passenger, sailing from the Port of Southampton, England, to the Port of New York. After a brief stint working in a pencil factory in New York, he was employed as a pianist in cafés and restaurants.

He eventually founded his own orchestra and published a few songs, which, despite their limited success, brought him to the attention of the Shubert brothers, who in 1914 hired him to write music for their Broadway theatre shows. That year he wrote his first successful Broadway revue, The Whirl of the World. He then contributed songs to several American musical adaptations of Viennese operettas, including the successful The Blue Paradise (1915). Even more successful was the musical Maytime, in 1917. Both involved love across generations and included nostalgic waltzes, along with more modern American dance music. At the same time, Romberg contributed songs to the Shuberts’ popular revues The Passing Show of 1916 and The Passing Show of 1918 and to two vehicles for Al Jolson: Robinson Crusoe, Jr. (1916), an extravaganza burlesque on the familiar story, and Sinbad (1918), an Arabian Nights-themed musical. Romberg wrote another Jolson vehicle in 1921, Bombo. He wrote the music for the musical comedy Poor Little Ritz Girl, which also had songs by Richard Rodgers.

Romberg married twice. Little is known about his first wife, Eugenia, who appears on a 1920 federal census form as being Austrian. His second wife was Lillian Harris, whom he married on March 28, 1925, in Paterson, New Jersey. They had no children. Lillian Harris was born March 8, 1898, and died April 15, 1967, in New York City.

Columbia Records asked Romberg to conduct orchestral arrangements of his music (which he had played in concerts) for a series of recordings from 1945 to 1950 that were issued both on 78-rpm and 33-1/3 rpm discs. These performances are now prized by record collectors. Naxos Records digitally remastered the recordings and issued them in the U.K. (They cannot be released in the U.S. because Sony Music Entertainment, which is a parent company of Columbia Records, holds the copyright for their American release.) Much of Romberg’s music, including extensive excerpts from his operettas, was released on LP during the 1950s and 1960s, especially by Columbia, Capitol, and RCA Victor. Nelson Eddy and Jeanette MacDonald, who appeared in an MGM adaptation of The New Moon in 1940, regularly recorded and performed his music. There have also been periodic revivals of the operettas.

Romberg died in 1951, aged 64, of a stroke at his Ritz Towers Hotel suite in New York City and was interred in the Ferncliff Cemetery in Hartsdale, New York.

Since 1970, Belišće organizes musical evenings in Romberg’s honor; similar events are held in Osijek since 1995. He was named as one of the meritorious and notable citizens of Osijek. Romberg was inducted into the Songwriters Hall of Fame in 1970.