The baby was born on the bathroom floor of his home in Gloucestershire, south-west England, around 6 pm, after he “arrived very quickly”.
“It was running to the gym, picking up a mat, going into the bathroom, putting the mat on the floor, dropped towels, brace, brace, brace,” said Tindall.
The baby, named Lucas Philip, weighed 3.6 kg at birth, a spokesman for the couple told CNN.
The couple’s other two children, Mia Grace and Lena Elizabeth, were not at home on Sunday for the newcomer, but have seen him since and are “in the clouds,” said Mike Tindall.
The midwife, who was supposed to meet them at the hospital, entered the scene quickly because she was not far, and a second came “when the head arrived”, he added.
Queen Elizabeth and her husband, the Duke of Edinburgh, are “delighted with the news” and hope to see the newest addition to the family when “circumstances permit,” a Buckingham Palace spokesman told CNN.
Zara is feeling healthy, said Tindall, and went for a walk with the baby.
“She was a warrior, as always, they always are,” said Tindall. “We can never judge a woman in terms of what she went through in childbirth.”
He said there are advantages to giving birth at home. After Lucas arrived, Tindall watched an old game of rugby and some golf with his new son.
Zara Tindall is a talented equestrian, having won the silver medal in a team event at the London 2012 Olympic Games.
She met her future husband during the 2003 Rugby World Cup, when he was playing for England. The couple married in Edinburgh in 2011.
Amy Cassidy of CNN contributed to this report.