Last, who sold more than 80 million records worldwide, was best known for pop hits in a big band style.
His trademark "happy sound" included a strong dance beat, crowd noise and laughter blended into the tunes. His first album, entitled "Non Stop Dancing", was released in 1965.
Born in the northern German city of Bremen, Last was originally a piano player and after World War Two he began a musical career that lasted some six decades.
Popular around the world, he appeared at London's Royal Albert Hall earlier this year.
Last "lived for music and wrote musical history", said Semmel Concerts, adding he was the most successful German band leader of all time.
"In him, the world loses a unique ambassador whose strong and all-embracing language was music," it added.
Last died in the presence of his family in Florida on Tuesday (local time) after a short illness, the firm said. A memorial service will take place in Hamburg, probably in the coming weeks.
