Princess Sofia gave birth to her and Prince Carl Philip's second child on Thursday last week.
His name was revealed after 11am on Monday at a meeting at the Royal Palace in Stockholm, attended by several senior representatives including Crown Princess Victoria and Prime Minister Stefan Löfven.
The King added that the new prince has been given the title Duke of Dalarna. His mother Sofia grew up in the Älvdalen area of Dalarna in west-central Sweden, famous for its almost-forgotten ancient language Elfdalian.
Prime Minister Stefan Löfven, Crown Princess Victoria and King Carl XVI Gustaf. Photo: Anders Wiklund/TT
One of the prince's middle names – Walther – honours Queen Silvia's father Walther Sommerlath, who died in 1990, while Carl is a common name among male members of the Swedish royal family.
It was not revealed why Carl Philip and Sofia chose the name Gabriel, which is not a traditional royal name in Sweden.
"We've seen the little one, and... it was a Gabriel," commented a smiling Löfven.
Gabriel is the younger sibling to Prince Alexander, who was born in April 2016, and the latest chapter in a Swedish royal baby boom in recent years.
Prince Oscar, the second child of princess Victoria, was also born in 2016. He is the younger brother of five-year-old Princess Estelle.
London-based Princess Madeleine meanwhile revealed only last week that she is pregnant with her and her husband Chris O'Neill's third child, the younger sibling of Prince Nicolas and Princess Leonore.
Monday was an eventful day for royal fans across Europe. In the UK, the Duke and Duchess of Cambridge announced that they are expecting their third child.
The first picture of Prince Gabriel, with his parents Prince Carl Philip and Princess Sofia. Photo: Royal Court