The couple took to Instagram to share the news by posting a video of them performing "My Girl," the Temptations' 1964 classic single.
"My Girl....Coming July 2017," Grammer captioned the clip, along with a baby emoji.
Grammer and Lise, who tied the knot in 2012, had previously said that their pregnancy is "really exciting, because on both sides of our family, it's the first girl.