L.K. Advani, Uma Bharti, and Murli Manohar Joshi of the Bharatiya Janata Party (BJP) will stand trial in the case.
They and five other Hindu leaders -- two of whom are now dead -- are accused of taking part in a 1990 criminal conspiracy to demolish the Babri Masjid in the northern town of Ayodhya.
It was torn down in December 1992 by a mob of Hindus, many using crowbars or bare hands.
The court ruling came after the Central Board of Investigation (CBI)
told India's top court on April 6 that Advani and the other accused had not faced conspiracy charges due to technical reasons.
According to the Supreme Court ruling, the crimes, which were allegedly committed nearly 25 years ago, shook "the secular fabric of the Constitution of India."
"The accused persons have not been brought to book largely because of the conduct of the CBI in not pursuing the prosecution of the aforesaid alleged offenders in a joint trial, and because of technical defects which were easily curable, but which were not cured by the State Government," it read.
"What is being done by us today is only to remedy what was expected by the Allahabad High Court to have been done shortly after its Judgment dated 12th February, 2001," it said.
The Supreme Court ruled that the trial must conclude within two years.
The decision will come as a blow to the Hindu nationalist BJP, which wants to build a temple on the site.
The BJP issued a statement Thursday saying essentially nothing had changed.
"This is almost akin to a status quo. Since 1993 this case has been going on," Sambit Patra, BJP spokesperson told CNN.
"As far as the criminal conspiracy case is concerned, it had gone to the trial court, it had gone to the High Court as well and now the Supreme Court has redirected back to the trial court."
Destruction of mosque led to revenge attacks
The Babri Masjid was built on a disputed site in Ayodhya in the 16th century and the town has been a religious flashpoint for more than 400 years.
Some Hindus believe it is where Lord Rama, one of the most revered deities in Hinduism, was born. Muslims claim the land because the mosque was built there in 1528.
The 1992 demolition sparked religious riots across the country in which more than 2,000 people died.
Dozens of temples and mosques were also targeted in a series of revenge attacks by Hindu and Muslim mobs.
The violence was some of worst seen in India since the bloody clashes that accompanied partition following independence in 1947.
Last month, Prime Minister Narendra Modi appointed the polarizing Hindu priest-turned-politician Yogi Adityanath
as chief minister of Uttar Pradesh, where Ayodhya is, raising concerns about the country's direction.
Modi, a member of BJP, has himself been criticized
for being complicit in a separate spate of violence in the state of Gujarat in 2002, in which more than 1,000 people were killed. Modi was at that time the chief minister of the state.
He was accused of not having done enough to halt the anti-Muslim violence, though a Supreme Court-ordered investigation absolved him of blame in 2013.