The ring at the door of the modest east Amsterdam apartment came late in the day on Thursday 14 March. On the doorstep stood two men “with contacts in the underworld”, Arthur Brand recalls, and with them a large, rectangular package.

Eagerly, Brand removed the covering and examined the contents: Buste de femme (Dora Maar), a portrait by Pablo Picasso of his mistress. Unsigned because it was never sold by the painter, it bore in its bottom-left corner the date he completed it, 26 April 1938, and was worth an estimated €25m (£21.5m).

“I don’t make much money at this game,” Brand, the detective known to the international media as the Indiana Jones of the art world, said. “But sometimes, you know, I can get rich emotionally. This is such a beautiful painting. One of Picasso’s personal favourites; it was hanging in his home when he died in 1973. And now it was in mine.”

So he thanked his two visitors, took another, rather less special canvas from the wall, and hung the Picasso in its place. He sat and looked at it until late in the evening, smoking. “Just for one night,” he said, “my flat was the most valuable in Amsterdam. And of course I could tell no one, because the painting was stolen.”

The next morning, representatives from an insurance company came and took Buste de femme away. An expert from New York’s Pace gallery, which had sold the painting on behalf of the Picasso estate to a Saudi prince in 1980, and Dick Ellis, the retired founder of Scotland Yard’s art and antiquities squad, verified its authenticity.

Missing since 1999, when it had been stolen from Sheikh Abdul Mohsen Abdulmalik al-Sheikh’s superyacht, the Coral Island, in the French Riviera port of Antibes, the work was long thought lost or destroyed. Despite a €400,000 (£344,000) reward, a French police investigation got nowhere and the case was eventually shelved.

Then, three years ago, word reached Brand of a stolen Picasso that had been “bobbing around in the Dutch underworld, apparently since about 2002”, and he began putting out feelers. Perhaps the world’s best-known art detective, the 49-year-old Dutchman has made headlines with a string of high-profile successes.

In 2015 he recovered a pair of massive Nazi-era bronze horses by Josef Thorak, one of Hitler’s favourite artists, which once flanked the entrance of the Reichstag in Berlin and had been believed destroyed by the Soviet army in 1945. The following year, he secured the return of a 1941 Salvador Dali and a 1929 Tamara de Lempicka snatched by masked men from a Dutch museum in 2009.

In 2016, Brand also negotiated successfully with criminals in Ukraine to recover five 17th-century Dutch masterpieces taken a decade earlier from another collection in the Netherlands, while last year he tracked down a spectacular 1,600-year-old Byzantine mosaic stolen from Cyprus in the 1970s.

Picassos, he said, did not generally excite him much: there are too many of them, and too many fakes. But the backstory to this one sounded interesting. At a meeting in an Amsterdam cafe, “a certain property developer” confessed to having briefly held the painting as collateral in a deal. Brand felt he was getting warm.

“The guy no longer had it,” he said. “But I put the word out I was interested, and someone got in touch. They were desperate. There comes a point, you know, when a stolen artwork that’s circulating in the criminal community – security in a drugs deal here, part-payment in an arms deal there – just becomes a burden. Something to be got rid of. But what do you do with it?”

The kind of people Brand often deals with in such cases, he said, “obviously can’t sell the thing. They don’t want to go to the police because they’d be asked awkward questions. They don’t want to try to con some other underworld guy with it, because he might come back with a gun. And most of them, despite what you might think, don’t want to destroy it. I offer them a way out.”

Buste de Femme had probably changed hands “10 or 20 times” since its theft, Brand estimated. “Some likely didn’t know it was stolen, certainly at first,” he said. “After all this time, all those changes of ownership, there’s no chance of catching the original thieves. Surely the most important thing is just to get the painting back.”

Fortunately, the Dutch police – with whom Brand works very closely – agree. “They confirmed the current owner of the painting wouldn’t be prosecuted,” he said. “So I told the intermediaries to hurry up. After 20 years in the underworld, the painting would not be in good condition. They should move fast. They did.”

Such high-profile successes have brought Brand an international reputation but little money. He has 10 or 15 stolen artwork projects on the go at any one time, but the bulk of his job, unreported, is helping Jewish families trace artworks that have been missing since the second world war, and advising wealthy clients on the provenance and authenticity of pieces they are considering buying.

But he would never give up the shadier side of his business – or the people it brings him into contact with. “I’ve never really felt threatened,” he said. “Maybe I’m too naive. They tell me I am. But if you’re straight and keep your word, they respect you and keep theirs. Often, we end up laughing.”

Brand only called one person that night when he had a €25m Picasso on his wall. “It’s a guy I have a drink with occasionally,” he said. “A guy who knows what it’s like to admire a stolen masterpiece, because he’s done it – Octave Durham, who snatched two priceless Van Goghs in Amsterdam a few years ago.”

Durham instantly asked him whether by any chance he was thinking of going out at some stage during the evening, Brand said. “I told him, ‘No chance. I’m staying home. You’re not getting your hands anywhere near this one.’”