The Uefa secretary general polled 115 votes, 27 more than closest rival Sheikh Salman bin Ebrahim al-Khalifa.
Prince Ali bin al-Hussein (4 votes) and Jerome Champagne (0) were third and fourth respectively.
Blatter, who had led Fifa since 1998, stood down last year and was later banned from football for six years for breaching ethics guidelines.
Infantino is a 45-year-old lawyer from Brig in the Valais region of Switzerland, less than six miles from Blatter’s hometown of Visp.
He only entered the presidential race when it became clear that Michael Platini, boss of European football’s governing body Uefa, would not be allowed to stand.
The election was due to be fought between five candidates, but South African Tokyo Sexwale withdrew before voting began in Zurich.
An emotional Infantino told delegates that he was finding it hard to “express my feelings in this moment”.
But he told delegates that together they would “restore the image of Fifa and the respect of Fifa”.
He added: “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.”