The Uefa secretary general succeeds fellow Swiss Sepp Blatter, polling 115 votes, 27 more than closest rival Sheikh Salman bin Ebrahim al-Khalifa, at Friday’s election.
Blatter quit in May amid allegations that led to a six-year ban from football, which he is contesting.
“I said today we have to build bridges, not build walls,” said the 45-year-old.
“Football can certainly do that. I want to focus on football,” he added.
The resignation of Blatter, who denies any wrongdoing, prompted the extraordinary congress at Fifa, which has been engulfed by claims of widespread corruption since summer 2015.
Infantino is a lawyer from Brig in the Valais region of Switzerland, less than six miles from Blatter’s hometown of Visp.
“Today it was an election, but not a war,” he said. “It was a competition, but not a fight. It was a sporting contest. An election you win, you lose and then life goes on.
“Now we turn the page, we start to work, we work good together and I show the whole world I’m not a candidate of Europe or wherever. I’m a candidate of football and football is universal.
“This is what we’ll start to do now in Fifa to work with everyone for the development of football and not to do politics, to speak about divisions, to speak about barriers.”
The first round of voting failed to determine an outright winner, though Infantino led with 88, three more than pre-vote favourite Sheikh Salman.
A simple majority of more than 50% – 104 of 207 available votes – was sufficient for victory in round two.
To help the new president tackle the crisis at Fifa, key reforms were passed to help make it a more transparent and accountable organisation.
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