The Great North Run founder and veteran track runner said it was a "real honour" to receive the royal accolade at Windsor Castle, where he was reunited with Anne.
The 73-year-old, who also established himself as a commentator, became European champion at 5,000 metres in 1974, and was made BBC Sports Personality the same year.
Sir Brendan, from Hebburn, went on to win 10,000-metre bronze at the Montreal Olympics, Great Britain's only track-and-field medal at the event, and took gold at the 1978 Commonwealth Games.
He was knighted for services to international and national sport and to culture in the North East.
"It's a real honour to be knighted today,” he said.
"It was particularly exciting for me to receive it from Princess Anne.
"We go back a long way. We were both on the Olympic team in 1976, we were both BBC Sports Personality of the Year in the 70s.
"It was lovely to see her and it was great to receive the honour from her."
Asked what they discussed, he said: "She said I deserve it for what I have done for sport, and not only the number of miles I have run. We go back 50 years, almost.
"She was in the showjumping team in the 1976 Olympics in Montreal and I was on the athletics team.
"She has been a great mover in the Olympic movement, she has been a great member of the Olympic committee and instrumental in bringing the Olympics to London in 2012.
"She has done amazing things both for her sport and for British sport, so she's a true sporting legend."
Sir Brendan said his personal sporting highlights were becoming European champion, Commonwealth champion and Olympic medallist in 1976.
"The sport has come a long way since then, but they would be my athletic highlights, and commentating on the Olympic Games in London in 2012 when Mo Farah won two gold medals," he said.
"It has changed hugely, because in our day it was an amateur sport. It's now a professional sport.
"The London Marathon and the Great North Run when I was running didn't exist, and they are both now pillars of the athletic world.
"More people are doing the sport, millions of people are taking part in mass running events around the world, so that's been the biggest change and that's been the most rewarding."