The 28-year-old midfielder has signed for Blues for an undisclosed fee and has penned a two-year contract at St Andrews.
Beginning his career at Ipswich before making a big money move to Newcastle United, Ambrose had spent the past three seasons with Palace.
He joins Peter Lovenkrands, Hayden Mullins and David Lucas in making the move to St Andrews following the lifting of the club's transfer embargo last week.