Tyler Dooley, 25, allegedly fled from security guards after handing in the four-inch lock-knife, but was later confronted by officers at his hotel nearby.
He then handed police a pepper spray.
He was celebrating his aunt’s wedding with his brother TJ and others at the Bacchus bar in Kingston upon Thames.
Mr Dooley is the son of Thomas Markle Jr, Meghan’s half-brother, who is divorced from his mother Tracey.
Scotland Yard said in a statement: “Police were called by security to a club in Union Street, Kingston upon Thames, in the early hours of Sunday, 20 May, after a man openly declared he had a knife as he attempted to enter the club.
“When officers arrived at 1.55am enquiries led them to a hotel in Kingston and two men in their 20s were spoken to by officers in connection with the incident.
“One of the men also voluntarily surrendered a noxious spray.
“Both men, who were visitors to the UK, were warned about their actions.
“Neither was arrested, no further action was taken and enquiries are complete.”
Carrying any lock-knife without a good reason is a criminal offence and can lead to a prison sentence. The law does allow possession of a knife with a folding blade three inches long or shorter.
South West BCU Commander Sally Benatar said: “We take the possession of knives and prohibited weapons very seriously and we are determined to take them off the streets.
“In this case, careful consideration was taken by the officers, the items were handed over voluntarily and there was no ongoing risk so the investigation was closed with warnings given.
“Having reviewed the circumstances and the risk posed by these two men, I support the actions taken by the officers.”
The club manager Lewis Mason said it had a zero tolerance approach to knives at the venue.
He said: “We don’t allow knives into the club.
“We call police if we find one we consider is illegal.
“We are working with police and awaiting the outcome.”
Apart from Meghan’s mother Doria Ragland, none of the new Duchess of Sussex’s family was invited to the Windsor Castle wedding which was attended by 600 guests and watched on television by millions around the world.
Like many of her relatives, Mr Dooley, an American, is estranged from his aunt Meghan and has not spoken to her for many years.
He and his brother and mother arrived in London a few days ago after reports they were to act as commentators on the royal wedding for the ITV channel.
They had already been interviewed on Good Morning Britain from their home in Oregon, where Tyler is involved in the legal farming of marijuana.
It was later reported that ITV had dropped any plans to include the family in its wedding coverage.
Hours after the incident, Tracy Dooley posted photographs on social media of her and Tyler at Hampton Court.
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She also posted pictures of the royal wedding and wrote: “Blessings and love to the Royal Couple! Thank you London for such a welcoming stay, love it here!”
When Sky News first asked Scotland Yard about the knife incident on Sunday night, a spokesman said there was no record of it.