Stepping into Mr Prince's place is Robert Rubin, former US Treasury Secretary, and Sir Win Bischoff is named as acting chief executive.
In a memo to his employees, reported by Reuters, Mr Prince said: "The size of these charges makes stepping down the only honourable course for me to take as chief executive officer. This is what I advised the board."
The bank is expected to write down $5 billion to $7 billion of sub-prime mortgages, after tax, but these figures may worsen.
Mr Prince's departure follows that of Stanley O'Neal, chief executive of Merrill Lynch, who was forced to resign following write downs of $8.4 billion.
Shares in the US bank have dropped by 32 per cent this year and 17 per cent since Mr Prince took over as chief executive in October 2003.