LeTang co-choreographed the hits Sophisticated Ladies and Eubie, both of which earned him Tony Award nominations. In 1989, he won a Tony for his work on Black and Blue. His other Broadway credits include My Dear Public, Dream With Music, Shuffle Along, and The Wiz (for which he choreographed the Tin Man's number, "Slide Some Oil to Me").
He also choreographed the films Tap, Bojangles, and The Cotton Club, and worked with such notable dancers as Gregory Hines, Debbie Allen, Maurice Hines, Savion Glover, and Chita Rivera.
In February 2003, LeTang was awarded an honorary doctorate by the Oklahoma City University School of American Dance and Arts Management.
LeTang was predeceased by wife, Ellie, who died in 2002. He is survived by his sons, Henry LeTang, Jr. and Jon LeTang.