Infantino has served as president since his election in February 2016 to complete the term of his predecessor, Joseph Blatter, who is serving a six-year football ban.
Infantino told the 211-member association before the vote that FIFA had come a long way since being embroiled in a series of corruption scandals that helped bring down Blatter in 2015.
"The last three years and four months were of course not perfect, I have definitely made mistakes," he said.
"I have tried to improve myself but today no one speaks about crises. No one speaks about scandals, no one speaks about corruption any more."
For the first time since 2007, when Blatter was re-elected for his third term, there was no election vote after delegates agreed to change statutes and allow an acclamation.
Infantino praised positive financial developments and transparency at FIFA, saying it was "no longer possible at FIFA to hide figures ... we know exactly where every dollar comes from and where every dollar goes".
Helped by revenue from the 2018 World Cup in Russia, FIFA reported a surplus of more than $1bn in the 2015-2018 cycle.
Revenue from the 2018 World Cup alone was $4.6bn, up $1.7bn from the previous tournament.
However, for 2020, FIFA expects a loss of $624m.
Reserves, which had fallen below the billion dollar mark for the first time in 2017, rose to a record $2.7bn at the end of December 2018, much higher than the expected growth of $1.6bn.
FIFA's corruption scandals, which led to Blatter's downfall and criminal charges against a number of FIFA and other officials, had caused financial problems for the governing body, among other things due to high legal costs.
In addition, a number of sponsors did not renew contracts.
Infantino said that after experiencing its "worst crisis", FIFA now had "a solid financial situation as never before".
He promised member associations would continue to benefit after receiving $1.1bn between 2015 and 2018, up from $326m in the previous cycle.
Now, $1.7bn is earmarked for the association in the period to 2022 through FIFA's Forward Development Programme, and FIFA will be checking closely how the money is spent, Infantino said.