The couple have named their son Lucas Philip Tindall in honour of Zara's grandfather Prince Philip, who will celebrate his 100th birthday on 10 June.
WATCH: Mike Tindall reveals the birth of his baby boy on his podcast
Zara's cousin, Eugenie, gave birth to her first child on 9 February and she and husband Jack Brooksbank named their son August Philip Hawke, also paying tribute to the Duke of Edinburgh.
Prince Philip was discharged from hospital last week following a four-week stay. He returned to Windsor Castle on 16 March after undergoing a heart procedure at St Bartholomew's on 3 March.
Mike and Zara's baby boy is the Queen and Prince Philip's tenth great-grandchild and the first grandson for Princess Anne. The couple are already parents to Mia, seven, and two-year-old Lena.
Eugenie and Zara have chosen the middle name Philip for their sons
Former rugby star Mike revealed his son was born on the bathroom floor at their Gatcombe Park home, after they were unable to make it to the hospital.
Speaking on his podcast, The Good, The Bad & The Rugby, Mike said: "Arrived very quickly. Didn’t make it to hospital. On the bathroom floor."
Mike and Zara are parents to Mia and Lena
Tindall described how he rushed to get a mat for his wife.
"So yeah, it was running to the gym, get a mat, get into the bathroom, get the mat on the floor, towels down, brace, brace, brace."
The tot is 22nd in line to the throne after his older sister Lena, although like his mother, baby Lucas is not likely to grow up to be a working royal.
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