According to the UK daily The Times, London paid Bank Mellat "1.25 billion pounds sterling ($1.54 million) with interest".
The settlement was announced on Twitter by Tehran's ambassador to London Hamid Baeidinejad.
"The compensation... has been paid," Baeidinejad tweeted, without specifying the amount of the payout, adding that it "represents an important legal victory for Iran".
In June 2013, the UK Supreme Court quashed a treasury directive imposing sanction on Bank Mellat over alleged links with Tehran's controversial nuclear programme. The judges ruled the sanctions "illegal" in the court's directive. According to The Times, which did not reveal its sources, the British government "reached a private settlement" in June with Iran over the sum owed to Bank Mellat after the Supreme Court decision.
The semi-public financial institution "had sought 3.2 billion pounds sterling but this fell to 1.25 billion pounds sterling with interest", The Times wrote.
Iranian state news agency IRNA reported the compensation agreed with London in June was $1.6 billion, without saying explicitly that this amount was paid.
The UK Treasury sanctions against Bank Mellat were part of a series of measures taken by Western nations against Iran after accusing Tehran of pursuing an atomic weapon under the cover of a civil nuclear programme.
These sanctions were lifted as part of a landmark 2015 deal between Tehran and world powers to curb its nuclear ambitions. The US unilaterally pulled out of the deal in May 2018, reimposing biting economic sanctions on Iran. According to The Times, "the payment (to Bank Mellat) was made through a third country and entity to evade US sanctions".
Since May, Iran has ceased to comply with certain commitments it made as part of the nuclear deal. Tehran says it is ready to recommit to the accord if European states help combat the impact of US sanctions, in particular regarding the export of its oil.