With almost all votes counted, Paz, of the Christian Democratic Party, defeated right-wing candidate Jorge "Tuto" Quiroga in Sunday's run-off election with a share of 54.6%. BBC reported.
A severe economic crisis and infighting within Mas, which has dominated Bolivian politics since 2006, saw many voters wanting change.
Paz has said he will end fuel shortages and address Bolivia's wider economic problems. In his victory speech, he said he would open up Bolivia to wider international investment and stimulate private-sector growth.
Paz,58, went from being a surprise frontrunner in the first round of the election in August to achieving a clear win over Tuto Quiroga, who received 45.4% of the votes in the run-off.
The candidate for Mas did not make it into the run-off.
Paz is perceived as relatively moderate and centrist compared to his opponent, making him more attractive to undecided and disillusioned left-leaning voters, who wanted change but did not want to cast their vote for Quiroga.
Quiroga has conceded defeat and has called his rival to congratulate him.
Paz's supporters took to the streets of La Paz, the country's administrative capital, to celebrate the result.
One of them told AFP news agency "we came to celebrate the victory with great hope of a new direction for Bolivia".
