But there is one thing the couple will keep a surprise: the gender!
"We don't know the sex of the baby," the SAG Award nominee revealed.
Even so, the couple -- who married in late 2014 after dating since 2012 -- have already started dreaming up baby names.
"In the middle of the night last night -- we arrived from London -- at 4 in the morning we started mumbling names to each other," Redmayne recalled. "We're two of the most indecisive people in the world!"