The former air stewardess, who suffered a miscarriage at the end of 2010, is in her second trimester.
Grammer wed his new bride shortly after divorcing reality TV star Camille last February (11).
The former Frasier star and his British wife met on a flight to New York. The baby will be 56-year-old Grammer's fifth child and Kayte's first.
He became a first-time grandfather last year (11) when his eldest daughter, actress Spencer, gave birth to baby son called Emmett.
The actor's representative has confirmed the baby news to People.com.