Final results gave Mr Vazquez, from the governing Broad Party, 52.8%, compared with 41% for Mr Lacalle Pou, of the right-wing National Party.
Mr Vazquez, 74, is a cancer doctor who served as president from 2005-10.
He won the first round of voting in October with more than 46% of the vote but it was not enough for an outright majority.
Incumbent President Jose Mujica was barred by the constitution from running for a second consecutive term.
“Big shoes to fill”
Speaking late on Sunday, Mr Vazquez called on the opposition to join him in a national accord to tackle the key issues the country was facing.
“I want to be able to count on all Uruguayans, but not so that they follow me but so that they guide me, accompany me,” he said.
In the capital Montevideo, thousands of his cheering supporters poured into the streets to celebrate.
Mr Vazquez has pledged to boost social spending and keep the economy in its current good shape.
He also wants to reform the education system and fight crime – two of the weakest points of Mr Mujica’s government, the BBC’s Ignacio de los Reyes in Montevideo reports.
Mr Mujica, who is also a member of the Broad Party, remains popular for leading the country through a period of economic growth and introducing social reforms such as legalisation of marijuana, abortion and gay marriage.
Mr Mujica refused to live in a palace when he became president four years ago and instead stayed at his humble farm in the outskirts of Montevideo, where he grows his own vegetables.
His down-to-earth style has put Uruguay in the international spotlight and his shoes will be hard to fill, our correspondent says.