Brenner, who appeared on "The Tonight Show with Johnny Carson" more than any other guest, died Saturday, the Hollywood Reporter said.
"Brenner died peacefully at his home in NYC surrounded by his family at his side," a statement from the comedian's longtime publicist Jeff Abraham said.
Abraham said as a last request, Brenner, "asked that $100 in small bills be placed in his left sock 'just in case tipping is recommended where I'm going.' His final resting spot will read, 'If this is supposed to be a joke -- then I don't get it!'"
Comedian Richard Lewis tweeted: "Brenner was a star. The king of 'hip, observational comedy' ... He was family. This leaves an irreplaceable hole."
Brenner made his debut on The Tonight Show on Jan. 8, 1971.
"Everything was perfect. You couldn't write a better scenario," Brenner said of the experience. "The next day, I had $10,000 worth of job offers. I never thought this was going to turn my whole life around."
During his career, Brenner was also featured on "The Ed Sullivan Show," "The David Frost Show," "The Mike Douglas Show," "Late Show With David Letterman," "Real Time With Bill Maher" and "The Daily Show."
Brenner is survived by his sons, Slade, Wyatt and Cole, wife Ruth and his grandson Wesley.