He told timeslive.co.za after watching the win in Yokohama that it had been fantastic to be among the crowd and feel the excitement.
"It's been phenomenal and the reality is that it's been phenomenal for South Africa and wonderful for the country," he said.
There was a feeling of déjà vu when thinking back to his side's 2007 triumph.
"I can't feel more proud than I am now thinking about the fact I've the privilege to watch them win another World Cup. It's three now," he said.
Coach Rassie Erasmus deserved praise for ensuring the Springboks stuck to their traditional forward strength. But White was also impressed that South Africa varied their play and asked questions from all over the field.
"South Africa played to their strengths. They picked a six-two bench with six forwards on the bench.
"The reality was that they were always going to play that way. They just stuck with what they did well for the whole competition," he said.
Before the game he had spoken at a function and pointed out that it was strange the Springboks went into the game as underdogs because, not only were they winners of the Rugby Championship in 2019 but they had also beaten the Six Nations champions Wales.
"South Africa have incredible strength, they have a massive pack of forwards while [wings] Cheslin Kolbe and Makazole Mapimpi were excellent. It was a phenomenal performance," White said.
Archbishop Desmond Tutu said the win restored a 'self-doubting nation's belief'.
"What a fantastic achievement, Siya Kolisi, Rassie Erasmus, and all the players and staff. You have achieved much more than winning a Rugby World Cup; you have restored a self-doubting nation's belief," he said in a message to the team.
"We are a special country, and an extraordinary people. On days such as this we understand that when we pull together the sky is the limit. When we believe in ourselves we can achieve our dreams. Our father, Nelson Rolihlahla Mandela, is smiling from the heavens today," he said.
Also joining in the delight was tennis great Roger Federer, whose mother Lynette, is South African. He posted on Twitter: "Maximum respect for all rugby players, amazing toughness and fairness.
"South Africa you did it! World Cup Champions, wow! I am incredibly happy," he said.