Memon was hanged at a prison in Nagpur in the western state.
The serial blasts killed 257 people, and were allegedly to avenge the killing of Muslims in riots a few months earlier.
India rarely carries out death sentences – only three people have been executed since 2004.
There was tight security around the Nagpur prison on Thursday morning, and in parts of the state capital, Mumbai.
The March 1993 blasts targeted a dozen sites, including the Bombay Stock Exchange, the offices of national carrier Air India and a luxury hotel.
Memon was hanged hours after the supreme court dismissed a final plea to stay the sentence.
His lawyers had argued that executions can only be carried out after seven days have passed following the rejection of a mercy petition.
But in a pre-dawn hearing, the court ruled that because his first mercy petition had been rejected last year, the execution met the required rules, said media reports.
Memon, a chartered accountant, was sentenced to death in 2007 by a special court in Mumbai after being convicted of providing financial and logistical support for the bombings.
He was the only one of 11 people convicted for the bombings to have his death sentence upheld on appeal. The sentences on the others were commuted to life imprisonment.
The additional chief secretary of the state government confirmed to the BBC that Memon’s body would not be buried inside the prison compound, and would be handed over to his family once a post-mortem had been carried out.
Memon’s case has divided opinion in India, with many calling for the suspension of the death sentence.
Yakub Memon’s brother, Tiger, is widely seen as having been the mastermind behind the attacks, alongside gangland boss Dawood Ibrahim. Both remain in hiding.
Several influential journalists, politicians and members of civil society had sent a letter to the president asking for him to “spare him from the noose of the death for a crime that was master-minded by someone else to communally divide India”.