Her husband, Mike Tindall, who has captained the English rugby team, announced the birth during an episode of his podcast, "The Good, The Bad and The Rugby," published Wednesday.
The baby boy was born on the bathroom floor of their home in Gloucestershire, southwest England, around 6 p.m., after he "arrived very quickly."
"It was running to the gym, get a mat, get into the bathroom, get the mat on the floor, towels down, brace, brace, brace," said Tindall.
Zara Tindall is the daughter of Princess Anne, the Queen's second child, and a first cousin of Princes William and Harry. The arrival is the monarch's 10th great-grandchild and is 22nd in line to the throne.
The baby, named Lucas Philip, weighed 8 lbs 4 oz at birth, a spokesperson for the couple told CNN.
The couple's other two children, Mia Grace and Lena Elizabeth, were not at the house on Sunday for the new arrival but have seen him since and are "over the moon," Mike Tindall said.
The midwife, who was supposed to meet them at the hospital, was on the scene quickly because she wasn't far away, and a second came "as 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 allow," a Buckingham Palace spokesperson told CNN.
Zara is feeling healthy, Tindall said, and has been on a walk with the baby.
"She was a warrior, as always, they always are," Tindall said. "We can never judge a woman in terms of what they have to go through at childbirth."
He said there were advantages to giving birth at home. After Lucas' arrival, Tindall watched an old rugby game and some golf with his new son.
Zara Tindall is an accomplished equestrian, having won a silver medal in a team event in the 2012 London Olympic Games.
She met her husband-to-be during the 2003 Rugby World Cup when he was playing for England. The couple were married in Edinburgh in 2011.