According to Tasnim news agency, Infantino, 45, succeeds Sepp Blatter, who stepped down last year with the organization mired in allegations of corruption and wrongdoing.
"I cannot express my feelings in this moment," he told delegates.
"I went through an exceptional journey, met many fantastic people who love football, who breathe football. I want to be the president of all of you, of all 209 nations."
"I want to work with all of you to work together and build a new era where we can put football at the center of the stage."
Secretary General of European governing body UEFA, Infantino won the first round of voting but without the necessary two-third majority to secure an immediate victory.
He received 88 of the 207 votes with Sheikh Salman three behind on 85. However, in the second round of voting, Infantino secured 115 votes -- 27 ahead of Salman -- to claim victory, CNN reported.
Infantino takes over at a time where FIFA is enduring one of the most difficult periods in its 112-year history.