"Mother, father and baby are doing extremely well," said Crowe rep Grant Vandenberg, People Magazine reported Friday.
Crowe and Spencer, who married in 2003, are also parents of son Charles Spencer Crowe, 2.
Crowe announced Spencer was pregnant at the Golden Globes in January, telling the media on the red carpet, "Dani is pregnant again. ... She's due in July."
Crowe said Charles knew he had a little brother on the way.
"He knows where the baby is, in mommy's tummy, and knows that he was a baby once and there's another baby coming along," Crowe said.
"And we said, 'Bubba, what do you want to call your brother?' and his first option was Pumpkinhead. But then the next day, he revised it and he changed it to Stinky."