The FIFA presidential election entered a second round of voting for the first time in 42 years after Infantino of Switzerland secured more backing than pre-vote favourite Sheikh Salman bin Ibrahim al Khalifa of Bahrain in the first round, when a two thirds majority was required to win.
A simple majority of more than 50 per cent - 104 votes - was sufficient for victory in the second round.
And Infantino secured 115 votes to Sheikh Salman's 88 to become the second successive Swiss president, after Sepp Blatter.
The 45-year-old lawyer is from Brig in the Valais region of Switzerland, less than six miles from Blatter's hometown of Visp.
FIFA has its first new head since 1998, when Blatter was appointed for the first time.
Blatter was voted in on five occasions, including last May, but he stepped aside days later amid allegations which led to a six-year ban from football-related activity, which he is contesting.
His resignation prompted the world governing body's extraordinary congress in the most pivotal period of FIFA's 112-year history.
Infantino will serve the remaining term of office for which Blatter was elected last May, meaning there will be a further election in 2019.
He told congress: "Dear friends, I cannot express my feelings in this moment. I told you I went through a journey, an exceptional journey, a journey which made me meet a lot of fantastic people, who love football and breath football and live football every day.
"We will restore the image of FIFA and the respect of FIFA and everyone in the world will applaud us.
"I want to work with all of you together in order to restore and rebuild a new era of FIFA where we can put again football at the centre of the stage.
"FIFA has gone through sad times, moments of crisis, but those times are over. We need to implement the reform and implement good governance and transparency. We also need to have respect.
"We're going to win back this respect through hard work, commitment and we're going to make sure we can finally focus on this wonderful game that is football."
Five candidates had been in the running to succeed Blatter, but South African Tokyo Sexwale withdrew his candidacy moments prior to the first round of voting.
The four remaining candidates were vying for 207 votes from FIFA's member associations (Kuwait and Indonesia are suspended).
In the first round, UEFA general secretary Infantino secured 88 of the 207 votes cast, while Sheikh Salman received 85 votes, Prince Ali bin al Hussein 27 and Jerome Champagne seven.
None received the two thirds majority of 138, so voting continued.
It was the first time voting for the FIFA presidential election had reached a second round since 1974, when Joao Havelange of Brazil became the first non-European president ahead of England's Sir Stanley Rous.
Infantino was making his way through the room - and alphabet of member associations - posing for photos and shaking hands, while wearing a beaming smile, as delegates voted in the second round.
Infantino was backed by Europe, with the Football Association and Scottish FA making their backing public. He also had support from Jose Mourinho, Luis Figo, Sir Alex Ferguson and Fabio Capello.
Prince Ali received four votes in the second round and Champagne did not receive any.
Infantino paid tribute to his rivals.
He said: "We had a sporting competition. And it was a great sign of democracy in FIFA. I want to be the president of all of you, of all 209 national associations.
"I travel through the globe and I will continue to do this."