The event, occurring just after sunrise in many places, was the longest solar eclipse of the 21st century, lasting more than 4 minutes in some places in India and China.
In China, a total eclipse was viewed at 9:15 a.m. along the upper stream of China's longest river of the Yangtze, Xinhua reported.
In Bangladesh, despite cloudy weather, a total eclipse was observed in the northwestern corner of the country by tens of thousands of enthusiasts. The Panchagarh district, the nearest town to the central line of the Umbra, had been designated the Capital of the Total Solar Eclipse.
For devout Hindus in India, the eclipse was an extraordinarily solemn occasion demanding strict discipline during its observance.
Pregnant women were not allowed to venture out, CNN reported.
For religious conservatives, consumption of food or even water was prohibited during the event.
Millions of Hindus took dips in sacred rivers like the Ganges in the belief they would wash away their sins so they can go to heaven. Varanasi, one of India's most sacred cities, was one of the places to witness the eclipse, the Hindustan Times reported.
Elsewhere in India, major Hindu temples closed to protect the sacred deities from any negative energy from the eclipse, other reports said.
Many of these temples receive hundreds of thousands of devotees daily.
In Kathmandu, capital of the mostly Hindu Himalayan republic of Nepal where people rise early, few were seen on the streets as they prayed at home for the protection of the sun god .