"I am really looking forward to meeting these arrivals," Grammer said.
These will be the first children for the couple, who suffered a miscarriage in fall 2010.
The ex-Frasier star, 56, has two children, 7-year-old Jude and 10-year-old Mason, with ex-wife Camille Grammer. He also has one daughter with Barrie Buckner, 19-year-old Greer, and one daughter with ex-wife Doreen Alderman, ex-Greek star Spencer, 28.
Grammer and Walsh Grammer, 32, tied the knot in New York last February.
