Alvin Ailey is a choreographer who was huge in popularizing modern dance in the American ballet scene. He also cast many African-American dancers, who often could not find work in traditional ballet companies. He based many of his works on music by blues and jazz musicians.
His ballet titled "The River" was a work of his set entirely to music by Duke Ellington.
Here's a narrative ballet by Alvin Ailey. It really gets going around 4.45. A less conceptual ballet, but very clearly a tribute to jazz.
On another note, a huge jazz center is being built in San Francisco called SFJazz.