Retired Met Police Ch Supt Matthew Gardner shared photos of Prince William on Rochester Row, in Westminster, on his social media account.
He said his brother-in-law, Richard Hannant, had seen what he thought was a celebrity and took a distanced photo.
Prince William then crossed the road and spoke to Mr Hannant while wearing the iconic Big Issue uniform.
The magazine is sold by homeless people, long-term unemployed people, and those who need money to avoid getting into debt, the Big Issue says.
Vendors are given five free magazines, which are then sold to the public for £3, with additional copies bought for £1.50.
Mr Hannant, a property manager, has since said he was on his way back to the office when he spotted the royal among a small group of people in the street.
The 47-year-old, who lives in Bath but works in London, said: "He was amazing, he was so friendly."
He added: "I think what struck me is we've just got past a massive Jubilee event and days later he's out there supporting a charity like Big Issue.
"I think it's that that I thought was most amazing because one is a worldwide event, this is just a low-key [event], literally standing on the side of the road with a homeless person.
"I was quite amazed that he could go from one massive event to such a low-key thing."
In his social media post, Mr Gardner wrote alongside the photo of his brother-in-law and the prince: "What an honour to have a private moment with our future king who was humble and working quietly in the background, helping the most needy.
"These 'silent gestures' often go unrecognised.
"The finale to this unique occasion was when Prince William asked my brother-in-law If he wanted to buy the Big Issue, to which he replied 'I have no change'.
"At this point William produced a mobile card machine… you cannot teach that!
"Priceless, or should I say, 'princely'."
Lithuanian tourists Vitalijus and Laura Zuikauskas also met the prince on their visit to London to celebrate the Queen's Platinum Jubilee.
"We bought the magazine and had a warm chat," said Mr Zuikauskas. "We wished him good luck and shook hands, and were excited that the Royal Family take big care of ordinary people."
He added the future king had a "warm personality" and they were "excited and really happy" to meet him.
Another social media post by black cab driver Neil Kramer also showed Prince William in the uniform posing for a photo with another Big Issue vendor.
He said: "I was charging up my taxi on Rochester Row in Westminster when I was approached by a vendor who introduced himself as William and asked would I like to buy a copy of the Big Issue.
"When I realised who it was, I was a bit shocked but of course said yes.
"He then introduced the other gentlemen with him and we had a lovely chat for 15 minutes about the charity and its work."
Mr Kramer said the prince asked him if he was a regular reader, to which he replied there was always an opportunity to buy the magazine when on a rank or charging up.
He added Prince William was engaging and polite, and that he never forgot his name.
The Duke and Duchess of Cambridge have previously spoken of their involvement with charities close to their heart, often inspired by his mother, the late Princess Diana.
In 2014, he visited homeless charity Centrepoint, while in 2018 the couple went to The Passage homeless centre in Westminster.
The Big Issue has been approached for a comment.