Police were put on alert nationwide ahead of the ruling, with thousands of extra security personnel deployed and schools closed in and around the northern city of Ayodhya, centre of the spat.
The verdict, which -- it is hoped -- will put an end to a bitter and at times arcane legal wrangle dating back decades, was due at 10:30 am (0500 GMT).
Hardliners among India's majority Hindus, including supporters of Prime Minister Narendra Modi's Bharatiya Janata Party (BJP), believe that Ram, the warrior god, was born in Ayodhya.
They say that in the 16th century, a Muslim emperor from the Mughal dynasty that ruled northern Indian for centuries built a mosque at the 2.3-acre (1.1-hectare) site.
In the 1980s, as Hindu nationalism and the BJP began to strengthen, pressure grew for the mosque to be knocked down and replaced by a vast Hindu temple.
In 1992, a Hindu mob estimated to number 200,000 did just that, reducing the 460-year-old mosque to rubble.
This unleashed some of the worst religious riots since India's bloody partition in 1947, leaving around 2,000 people dead, mainly Muslims.
Ten years later, 59 Hindu activists died in a blaze on a train from Ayodhya, sparking riots in Gujarat state -- when Modi was premier -- that saw upwards of 1,000 people perish.
In 2010, a High Court ruled that Muslims and Hindus should split the site -- albeit unevenly, with Hindus granted the lion's share.
Both Hindu and Muslim groups appealed and the Supreme Court in 2011 stayed the lower court's ruling, leaving the issue unresolved.
The BJP has campaigned for years for a temple to be built at Ayodhya, and a verdict clearing the way for that would be a major victory for the 69-year-old Modi, just months into his second term.
But it will also send shudders through many in the 200-million-strong Muslim minority who fear that the BJP is bent on turning India into a purely Hindu nation.
Modi is nevertheless desperate to avoid bloodshed and ahead of the verdict, the BJP and the more hardline RSS organisation have told supporters to avoid any provocative celebrations.
"Whatever is the verdict by the Supreme Court, it won't be anybody's win or loss," Modi tweeted late Friday.
"My appeal to the people of India is that our priority is to ensure the verdict strengthens the values of peace, equality and goodwill of our country," he said.
In addition to 500 arrests of would-be trouble-makers, Uttar Pradesh state police chief O.P. Singh told the Economic Times that 10,000 "anti-social" elements had been identified.
Around 16,000 digital volunteers from 1,600 villages in the region have also been enlisted to help monitor and flag contentious content on social media.
Already on Friday, a 56-year-old man in Maharashtra state was arrested for posting on Facebook that he hoped the verdict would remove a "dark spot of history", the Press Trust of India reported.