The 56-year-old monarch revealed that the pair were "overjoyed" and "thrilled" when they found out the life-changing news.
Prince Albert and Princess Charlene of Monaco
Speaking to the Associated Press at the opening of the new Monaco Yacht Club on Friday, he also revealed they were "very excited" to discover that their child would be born in December, but that they are "taking every cautious step to make sure everything goes well."
Albert and his wife Charlene, 36, announced their pregnancy at the end of May.
The Prince's Palace of Monaco released a statement confirming the happy news which read: "T.S.H the Prince and the Princess of Monaco are delighted to announce the pregnancy of H.S.H. Princess Charlene."
"The birth is expected at the end of the year," it continued.
Prince Albert and Princess Charlene of Monaco at their wedding in 2011
"Now I'm settled and I think kids will come. I don't put any pressure on myself," she told South African newspaper Sunday World.
"If it happens, it happens."
Princess Charlene showed off her baby bump on Friday"My husband is my biggest support, the person that I confide in and who knows me best," she said
In an exclusive interview with HELLO! magazine's sister publication, HOLA! in April, the former Olympic swimmer spoke of her husband as her "biggest support".
The new be the most recent addition to the Grimaldi family, after Prince Albert's niece, Charlotte Casiraghi, welcomed a baby in December 2013 with French comedy actor Gad Elmaleh. His nephew Andrea Casiraghi also welcomed a little boy earlier that year.