Than Shwe received a ceremonial welcome at the presidential palace in New Delhi and met with President Pratibha Patil at the start of a five-day visit.
The 77-year-old military strongman, who was responsible for a violent crackdown on pro-democracy protests in 2007, laid a wreath at a memorial to Mahatma Gandhi, leader of India's freedom movement and an icon of non-violent resistance.
After meeting Foreign Minister SM Krishna and Vice President Hamid Ansari, Than Shwe and Prime Minister Manmohan Singh began talks Tuesday evening.
Proposals to expand cooperation in energy, trade and counter-terrorism were expected to be signed, Foreign Ministry officials said.
Human rights groups condemned India's decision to accord an official invitation to the leader of a regime under sanctions from several Western countries for human rights violations.
The junta says it will hold elections this year but has disqualified opposition leader Aung San Suu Kyi and her National League for Democracy from the polls.
Delhi, which once backed Suu Kyi, has deepened its engagement with Myanmar's junta over the past decade, eyeing the country's rich hydrocarbon resources.
An Indian investment of over a billion dollars in Myanmar's gas and energy sectors could be announced after the talks, news reports said.
Besides counting on the junta's help to counter separatist rebels operating in its troubled north-east, India also hopes to counterbalance China's growing clout in Myanmar.
'Even as it loses out in its efforts to counter China's influence, India has mortgaged its voice on political and human rights issues in Burma,' Elaine Pearson of the New-York based Human Rights Watch said.
'Singh should make a point to publicly voice principled criticism over the rigging of Burma's electoral laws and continued restrictions on basic freedoms in Burma,' she added.
In Delhi, scores of Myanmar exiles and rights activists protested in central Connaught business district, demanding that India press the junta leader to initiate democratic reforms and release political prisoners.
'We feel outraged with his visit as India is the largest democracy in the world and the land of the Buddha and tolerance,' Tint Swe, a former member of the Burmese parliament and a pro-democracy activist told the IANS news agency.