Javad Marandi, who has an OBE for business and philanthropy, can be named after losing a 19-month legal battle with the BBC to remain anonymous.
Mr Marandi strongly denies wrongdoing and isn't subject to criminal sanction.
The judgement against him is a milestone for freedom of the press amid growing privacy laws in the courts.
A spokesman for the businessman said: "Mr Marandi is deeply disappointed at the court's decision to lift reporting restrictions, knowing the reputational damage that is likely to follow."
A National Crime Agency (NCA) investigation found some of Mr Marandi's overseas interests had played a key role in an elaborate money-laundering scheme involving one of Azerbaijan's richest oligarchs.
In January 2022, a judge ruled the NCA could seize £5.6m [$7m] from the London-based family of Javanshir Feyziyev, a member of Azerbaijan's parliament.
Their British bank accounts received cash that had been removed from Azerbaijan in what the judge said had been "a significant money-laundering scheme".
The family have denied that allegation - and at the outset of the hearing, in October 2021, Mr Marandi was granted anonymity in court.
Now, High Court judges have ruled that Mr Marandi can be identified because he had been a "person of importance" in the NCA's case.
Mr Marandi, 55, was born in Iran and grew up in London, where he still lives.
His ties to the Conservative Party emerged through reports of his generous donations. Between 2014 and 2020, he gave £756,300, according to Electoral Commission records.
In February 2022, the Sunday Times reported he was a member of a group of major donors who had access to senior party members, including to then prime minister, Boris Johnson.
Mr Marandi was described in court as a "highly successful international businessman" with a broad portfolio of business interests in the UK and abroad.
He owns the iconic design brand, The Conran Shop, a stake in Anya Hindmarch Ltd, the luxury handbag firm, and an exclusive private members' club and hotel in Oxfordshire.
Along with his wife, he heads the Marandi Foundation, which funds the Prince and Princess of Wales's charity.
In 2021, Mr Marandi became a special adviser to homelessness charity Centrepoint, providing guidance on how it could expand its work with disadvantaged young people.
None of Mr Marandi's UK businesses or these organisations form any part of the NCA's investigation, which looked at earlier events.
The probe began in 2017, after investigative journalists revealed an enormous money-laundering scheme, which became known as the "Azerbaijani Laundromat".
The Organised Crime and Corruption Reporting Project (OCCRP) revealed how $2.9bn (£2.3bn) of dirty money - cash stolen from Azerbaijan's people and economy - had been spirited away by members of the country's elite. It was largely for their own benefit, but also to bribe European politicians.
Paul Radu, the OCCRP's co-founder, said the Laundromat scheme was one of the most significant examples of post-Soviet looting.
"The Azerbaijani Laundromat brought a lot of damage on many levels to Azerbaijan itself, to the European Union, to the US, and other parts of the world," he said.
"Small businesses lost a lot of money - they had deposits with a bank that was at the centre of the Laundromat."
Those revelations prompted the NCA to investigate the Feyziyev family's finances in the UK - leading to its application, in 2021, to seize some of their UK cash - and the disclosure in court of the link to Mr Marandi.
According to documents from the NCA's case at Westminster Magistrates' Court, the suspect money that made its way to the Feyziyev family accounts in London had originated in bank accounts belonging to a company with neither employees, nor traceable records of its activities.
Based in Baku, Azerbaijan's capital, Baktelekom looked like a state-owned firm that has an almost identical name.
District Judge John Zani found that "substantial funds from this criminal enterprise" were then moved into two bank accounts in the Baltics belonging to Glasgow-registered shell companies.
Some of the cash was then moved onwards to accounts linked to Javanshir Feyziyev and Javad Marandi, according to the NCA.
A series of firms, sharing the name Avromed, were "central" to the transfer of this money.
One of them had been set up in the Seychelles in 2005, with Mr Marandi being its beneficiary.
Court papers show the Avromed Seychelles company received large sums, as shown in the graphic below.
Money flowed into the company from other sources. In total, investigators say it paid out:
* $34.8m (£27.8m) to Javanshir Feyziyez
* $48.8m (£39m) to Javad Marandi
* $106.9m (£85.4m) to Vynehill Enterprises, a British Virgin Islands company beneficially owned by Mr Marandi
Ruling on the NCA's application to seize cash from the Feyziyev family, the judge concluded: "I am satisfied that there is overwhelming evidence that the invoices and contracts purporting to support legitimate (and very substantial) business transactions between Baktelekom, Hilux and Polux were entirely fictitious."
They were produced in order to allow "very significant sums into and out of their accounts so as to mask the underlying money-laundering activities of those orchestrating the accounts".
The National Crime Agency told the court it would "neither confirm nor deny" whether there was an active investigation into Mr Marandi's finances - but the well-known businessman has adamantly denied any involvement in wrongdoing.
His lawyers told the court that between 2012-2017, tight currency controls in Azerbaijan meant he had to use exchange houses in Latvia and Estonia to transfer legitimately-owned dividends from Avromed and other businesses.
"The funds were lawfully earned, and lawfully transferred, and there is no question of money laundering," they said.
Legal battle: Began in October 2021 at outset of major NCA case
When the NCA's case against the Feyziyev family first went to court, Mr Marandi's lawyers argued that revealing his identity would breach his privacy and cause "profound and irremediable" damage to his reputation - not least because no law enforcement body had interviewed or approached him regarding the case.
After the court ruled the NCA could seize millions from the Feyziyev family's British bank accounts, the BBC and London Evening Standard argued it was in the public interest to disclose that some of Mr Marandi's overseas interests had been part of the case.
Judge Zani ruled, in May 2022, that Mr Marandi - who was referred to as MNL - could be named under principles of open justice, saying he had been a "person of importance to the main proceedings".
That ruling triggered more than a year of further challenges by Mr Marandi.
His lawyers succeeded in getting a costly High Court review of Judge Zani's ruling. By this stage, the London Evening Standard had dropped out of the challenge.
Last month, two of the country's most experienced judges ruled the media could name Mr Marandi.
They concluded that open justice was a fundamental principle and that anonymity should only be allowed in exceptional circumstances.
Mr Justice Mostyn said: "My only surprise is that the anonymity order was granted in the first place. For reasons of procedural unfairness as well as a distinct lack of merit, it should never have been granted."
Duncan Hames, director of policy at the anti-corruption research group Transparency International UK, said the Conservative Party had questions to answer.
"This is a political bombshell," he said. "We've learned today that someone who's given hundreds of thousands to a British political party has, in the words of the judge, been a person of importance in proceedings before the court about a major money-laundering enterprise.
"That should be a concern, not just to people who are worried about where that money came from, but about what it says about how easily money can reach political parties without [them] doing proper checks on on its origins."
The former Liberal Democrat MP added: "It's not good enough just to check whether someone is on the electoral roll. Our political parties need to be much more careful about who they take money from. "
BBC News has contacted the Conservative Party, The Royal Foundation and Centrepoint for comment.