The images, created by Joe Mullins, who has worked in forensics for 17 years, show a young girl with brown eyes and black hair, and a boy with blue eyes and brown hair.
The baby, who will be seventh in line to the throne, is due in spring 2019.
Kensington Palace revealed the happy news Monday after the newlyweds touched down in Australia for the start of a 16-day tour.
The queen said she is "delighted," while Markle's mother, Doria Ragland, said in a statement that she's "very happy at this lovely news and is looking forward to welcoming her first grandchild."
Ragland is reportedly planning to move to London to be closer to her daughter and first grandchild.
Markle's pregnancy is considered high-risk because she's 37 years old and there's also concern about her busy travel schedule. The couple flew from London to Australia via Singapore, and they were in the air for 22 hours.
"The main things for long air travel is to wear comfortable clothing, stay well hydrated with a lot of water and wear compression stockings to help prevent any risks for blood clots," OB-GYN Dr. Sherry Ross told Inside Edition.
Another concern is that the trip will include visits to Fiji and Tonga, where the Zika virus has been detected. The CDC recommends pregnant women not travel to areas where there is a potential risk of Zika.
"Regardless of who you are, we definitely recommend no destinations have any Zika virus because it's dangerous," Dr. Ross said.