The constitution - the central reform of Morales's three-yearold administration - won by a 59 percent to 41 percent tally, according to an unofficial quick count with a three-percentage point margin of error. A final official tally will be announced in 10 days.
Morales, an Aymara Indian and Bolivia's first indigenous president, has said the charter will decolonize South America's poorest country by recovering indigenous values lost under centuries of oppression dating back to the Spanish conquest.
Bolivia's Aymara, Quechua, Guarani, and dozens of other indigenous groups only won the right to vote in 1952, when a revolution broke up the large haciendas on which they had lived as peons for generations.
"The poorest people are the majority. The people with money are only a tiny few," said voter Eloy Huanca at a polling place in El Alto outside the capital of La Paz. "They ran things before, and now it's our turn."
But opposition leaders warn that the constitution does not reflect Bolivia's growing urban population, which mixes both Indian blood and tradition with a new Western identity.
They also object to Morales's vision of greater state control of the economy and his government still faces stiff opposition from Bolivia's eastern lowland states, which control much of the nation's wealth and largely voted against the charter.
"People will go to vote for the possibility of dreaming for a better country - but a country for all of us," said Ruben Costas, opposition governor of the eastern state of Santa Cruz. "We should all be part of this change."
Morales has allied himself closely with President Hugo Chávez of Venezuela in what they call "21st century socialism," sharing his anti-American rhetoric.
Last year, Morales booted out Bolivia's US ambassador and Drug Enforcement Administration agents after saying they had conspired against his government last year.
Yesterday's vote went peacefully, a relief for a nation where political tensions have recently turned deadly.
The proposed document would create a new Congress with seats reserved for Bolivia's smaller indigenous groups and would eliminate any mention of the Roman Catholic Church, instead recognizing and honoring the Andean earth deity Pachamama.
The charter calls for a general election in December in which Morales could run for a second, consecutive five-year term. The current constitution permits two terms, but not consecutively.
At the heart of the constitution is a provision granting autonomy for 36 indigenous "nations" and several opposition-controlled eastern states. But both are given a vaguely defined "equal rank" that fails to resolve their rival claims over land in Bolivia's fertile eastern lowlands, whose large agribusiness interests and valuable gas reserves drive much of the country's economy.
