Welch appeared in a number of shows on Broadway, including Blackbirds of 1928, which she later took to France; Runnin' Wild, in which she sang the now-famous "Charleston" song; and Cole Porter's The New Yorkers, in which she performed the once-scandalous "Love For Sale." She then began a long career in London, singing "Stormy Weather" in Dark Doings and introducing the song "Solomon" in Cole Porter's Nymph Errant, which starred Gertrude Lawrence. Welch also was seen on the London stage in Glamorous Night, Arc de Triomphe, Tuppence Colored, and No Time For Comedy with Rex Harrison and Lilli Palmer; her later appearances were in Cindy-Ella, A Marvellous Party, and Pippin.
She returned to Broadway in 1986 and received a Tony nomination for her work in Jerome Kern Goes to Hollywood. Welch also appeared in Black Broadway at Town Hall and won a Village Voice OBIE Award for her performance in Elisabeth Welch: Time to Start Living.
In addition to her stage work, Welch performed in the radio show Soft Lights and Sweet Music and in a number of films including Song of Freedom, Big Fella (with Paul Robeson), Revenge of the Pink Panther, and Derek Jarman's adaptation of The Tempest.