Cross posted from the BBC
Mr Morales said the road would no longer go through a rainforest reserve.
He made the announcement two days after protesters arrived in La Paz following a two-month march from the Amazon lowlands to voice their opposition.
It is not yet clear what the demonstrators’ response will be.
The president said he would send a measure to Congress that would accommodate the protesters’ demands.
“The matter is resolved,” Mr Morales said.
An indigenous leader, Rafael Quispe, said the president’s proposal was a “good sign” but said they had 15 other demands that needed to be discussed, the Spanish news agency Efe reported.
President Morales had been under fire ever since he announced his government’s plan to build the road, no matter what, says the BBC’s Mattia Cabitza in La Paz.
This is the second time in less than a year that Mr Morales has backtracked under popular pressure, our correspondent adds.
The last time, just after Christmas, was dubbed the “Gasolinazo”, when he tried to almost double petrol prices but was forced to drop the plan. Then, like today, he said he was “governing by obeying the people”.
Development – or disaster?
Thousands of residents were on the streets of La Paz this week as some 1,000 protesters arrived to call for the project to be stopped.
The government had argued that the road would boost economic development and regional integration.
The protesters said the project – funded by Brazil and built by a Brazilian company – would encourage illegal settlement and deforestation in their rainforest homeland.
The plans were for a highway through the Isiboro Secure Indigenous Territory and National Park – known by its Spanish acronym Tipnis.
President Morales, Bolivia’s first indigenous president, had already suspended the project and offered talks with the protesters.
However, there were also demonstrations in support of the road project from indigenous groups that are loyal to the president.