The couple say they are "overwhelmed with happiness" at the birth of Elijah Joseph Daniel Furnish-John.
John's spokeswoman Fran Curtis confirmed an announcement on the singer's website that the baby was born Friday in Los Angeles. The infant, born to a surrogate mother, weighs 8 pounds, 4 ounces (3.7 kilograms).
John, who is 65, and 50-year-old Furnish wed in a British civil partnership in 2005 and are parents to 2-year-old Zachary Jackson Levon Furnish-John, born in California in December 2010, also through a surrogate mother.
John told The Guardian newspaper last year that he hoped to have a sibling for Zachary because "it's difficult to be an only child, and to be an only child of someone famous."
John and Furnish told Hello! magazine Wednesday that "the birth of our second son completes our family in a most precious and perfect way."