The couple, who have been dating for a year after meeting at a party, are expecting their first child together in September, the News of the World reports.
A source said: "They have been keen to start a family for a while now. They're absolutely made up. We expect to hear wedding bells next year. Jacqui was crying with joy when she found out she's pregnant.
"They went on holiday because Guy is desperate she takes it easy. He won't let her do anything more strenuous than argue over baby names."
The film director already has two sons with ex-wife Madonna - ten-year-old Rocco and adopted David, six. He was allegedly paid a £60m settlement when they divorced in 2008.
A spokesperson for Ritchie and Ainsley declined to comment.