Alexander was born in London, England. He studied at Tri-State College in Indiana and Ryerson University in Toronto. Working as a cab driver, truck driver, speakeasy operator, waiter, tree salesman, marketing manager, ad salesman, magazine editor, and producer in the alternative theatre scene in Toronto positioned him well for a career in the Comedy Business. That chance came in 1974 when he became the head of The Second City in Toronto.
As leader of the Toronto theatre, Alexander produced and developed content for live theatre shows in collaboration with the legendary performers of the 1970s: Gilda Radner, John Candy, Dan Aykroyd, Andrea Martin, Catherine O’Hara, Eugene Levy, and Joe Flaherty, among others. Two years later, he forged a partnership with Len Stuart to create The Second City Entertainment Company, whose first production was the groundbreaking television show SCTV. After almost a decade developing the Entertainment Company, Alexander and Stuart became owners of The Second City Chicago in 1985. Since then, Alexander has actively led The Second City in Canada and the United States for over thirty years.