Amateur stargazers and scientists travelled far to see the eclipse, which lasted six minutes and 39 seconds at its maximum point. The eclipse could first be seen early on Wednesday in eastern India.
It then moved east across India, Nepal, Burma, Bangladesh, Bhutan, China, Japan and the Pacific.
The eclipse first became total over India at 0053GMT, and was last visible from land at Nikumaroro Island in the South Pacific nation of Kiribati. It ended at 0418GMT.
Elsewhere, a partial eclipse was visible across much of Asia.
Mixed blessing
In India, millions gathered in open spaces from the west coast to the northern plains, with clouds parting in some cities at dawn - just before the total eclipse.
 |   |
But thick clouds and an overcast sky obscured the view at the Indian village of Taregna, "epicentre" of the eclipse, says our correspondent in the area.
Many of the thousands of people who gathered there to watch the eclipse left the village disappointed.
"We were apprehensive of this cloudy weather but it was still a unique experience with morning turning into night for more than three minutes," scientist Amitabh Pande told the Associated Press news agency.
Some enthusiasts in India were on board a special chartered flight for a close-up view of the eclipse.
The BBC's Sanjoy Majumder, who was on the flight, said that from a vantage point of 41,000ft (7,756 miles), it was a celestial spectacle like few others.
Among the passengers were a man who was witnessing it for the eighth time, scientists, amateur astronomers and children.
In India and Nepal, where it is considered auspicious to watch the eclipse while immersed in holy water, crowds gathered at rivers or ponds, including tens of thousands of people at Varanasi on the Ganges.
"We have come here because our elders told us this is the best time to improve our afterlife," said Bhailal Sharma, a villager who had travelled to Varanasi from central India.
But for others, the eclipse was seen to be a bad omen.
In Nepal, authorities shut all schools for the day to avoid exposing students to any ill-effects, says the BBC's Joanna Jolly in Kathmandu.
 People bought masks to view the eclipse |
Some parents in Delhi kept their children from attending school at breakfast because of a Hindu belief that it is inauspicious to prepare food during an eclipse, while pregnant women were advised to stay inside due to a belief that the eclipse could harm a foetus.
"My mother and aunts have called and told me stay in a darkened room with the curtains closed, lie in bed and chant prayers," said Krati Jain, a software worker in Delhi who is expecting her first child.
Authorities in China, where an eclipse was a bad omen in ancient culture, reassured the public that services would run normally.
In the east of the country, heavy cloud or rain obscured it.
Pollution was also a barrier, with thick smog in Beijing blotting out the sky.
'Special opportunity'
The last total eclipse, in August 2008, lasted two minutes and 27 seconds.
Alphonse Sterling, a Nasa astrophysicist who followed the latest eclipse from China, said scientists were hoping data from it would help explain solar flares and other structures of the sun and why they erupt.
"We'll have to wait a few hundred years for another opportunity to observe a solar eclipse that lasts this long, so it's a very special opportunity," Shao Zhenyi, an astronomer at the Shanghai Astronomical Observatory in China told the Associated Press.
Solar eclipses allow scientists to see the gases surrounding the sun, or its corona.
Solar scientist Lucie Green, from University College London, was aboard an American cruise ship heading for the point near the Japanese island of Iwo Jima, where the axis of the Moon's shadow passed closest to Earth.
"The [Sun's] corona has a temperature of 2 million degrees but we don't know why it is so hot," she said.
"What we are going to look for are waves in the corona.
"The waves might be producing the energy that heats the corona. That would mean we understand another piece of the science of the Sun."
The next total solar eclipse will occur on 11 July, 2010. It will be visible in a narrow corridor over the southern hemisphere, from the southern Pacific Ocean to Argentina.
source bbc.co.uk