The couple said that they were "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 last Friday in Los Angeles.
The infant, born to a surrogate mother, weighs 8 pounds, 4 ounces (3.7kg).
John, who is 65, and 50-year-old Furnish wed in a British civil partnership in 2005 and are parents to two-year-old Zachary Jackson Levon Furnish-John, born in California in December 2010, also through a surrogate mother.
John and Furnish told 'Hello!' magazine that "the birth of our second son completes our family in a most precious and perfect way".