Earlier this week Mr Wasserstein was taken to hospital after suffering from an irregular heartbeat, but the precise cause of death has not yet been made public.
He had worked at investment bank Lazard since early 2002 and in 2005 was made chairman and CEO at the company.
Under his chairmanship, Lazard became the world's sixth largest advisor on global mergers and acquisitions, and managed to come through the financial crisis relatively unscathed, even increasing its market share.
Before joining the company, Brooklyn-born Mr Wasserstein had built a reputation as a legendary dealmaker.
In 1988 he co-founded advisory firm Wasserstein, Perella & Co, which was subsequently sold for more than $1.5 billion to Dresden Bank AG towards the end of 2000.
During his career, he brokered around $250 billion worth of transactions, including Warner Brothers's merger with Time and Morgan Stanley's deal with Dean Witter and Discover & Co.
Up until his death Mr Wasserstein was involved in negotiations relating to the proposed takeover of UK chocolate manufacture Cadbury by Kraft Foods.
Lazard's board of directors issued a statement in which they said they were deeply shocked and saddened by his death.
"He was a visionary leader, a devoted father to his children and a good friend," the statement said.
"Lazard's board of directors, and the many people he worked with and mentored over the years, mourn his loss."
Steven Golub, vice chairman of Lazard, has been named as interim CEO while the investment bank begins it search for a replacement for Mr Wasserstein.
Mr Golub, 63, joined the Bermuda-based firm in 1984 and was a close confidant of Mr Wasserstein.
He was made chairman of the company's financial advisory business in 2005, the same month that Mr Wasserstein became Lazard CEO.
By Claire Archer