The grandson of the Hollywood actress Grace Kelly, named Alexandre, is now almost two years old. His mother, Nicole Coste, is originally from the African nation of Togo.
"I recognised this child before a lawyer a few weeks after its birth," Prince Albert, who usually fiercely guards his privacy, said in remarks to appear in Le Monde's II magazine on Saturday.
"The child will therefore have a father and will lack for nothing," he said. "I will watch over this and will see him often."
Albert, 47, has no other children and is not married. He took over royal powers in the Riviera principality shortly before Prince Rainier III's death in April, and will formally assume the throne on 12 July.
Asked if the child would have the family name Grimaldi, Albert said in the interview: "No. His existence will have no effect on the functioning of the regime or on my succession.
"The rules of the constitution are very clear on this matter. There will be only patrimonial consequences." Under Monaco's constitution, only a child born in wedlock can succeed to the throne.
The Prince said he regretted that Paris Match magazine went public with the story just weeks after the death of his father, Prince Rainier, in April. "I find it saddening, shocking, that this affair - which should have remained strictly private - was made public in that way, and at that time," he told Le Monde.
In a cover story in May, Paris Match alleged Albert had fathered a son with Ms Coste. Ms Coste was quoted as saying she met Albert on a flight in July 1997, leading to a relationship and the birth of a child, Alexandre, in August 2003. The interview was illustrated with Pictures of the smiling prince holding and feeding a young boy.
Ms Coste, who lives in Paris, said she went public with the story because she wanted "Alexandre to grow up normally, with a father".
The Prince wanted to face up to his responsibilities, said a statement released by Albert's lawyer, Thierry Lacoste.
"That's why he recognised the child and hopes that he can live out his childhood and adolescence in a calm and protected setting, in strict isolation from the media," said a statement issued by the lawyer.
Albert said he was tired of fielding questions about why he was still single, and said he plans to have a family when he is ready. "Allow me to go at my own pace," he said. "But I assure you, I will get married."
He caused consternation to his father because of his refusal to wed, and the constitution was revised in 2002 to circumvent the problem posed by his only-child bachelor status.
If he has no legitimate heirs, the next in line would be Princess Caroline, the eldest of Albert's two sisters. She, in turn, would be succeeded by her oldest son, Andrea Albert Pierre.