Hofer admitted defeat in a note on his Facebook account, saying "You have supported me so magnificently and I am infinitely sad that it did not work out."
Hofer also congratulated Van der Bellen, former Green Party Leader, for the election victory. "I ask for all Austrians to keep together and work together."
He added: "We are all Austrians, no matter how we decided in the polls."
"I congratulate our new President Van der Bellen," Austrian Prime Minister Christian Kern said in a statement.
According to state-run broadcaster ORF, Van der Bellen received 53.3 percent of the votes while Hofer got 46.7 percent.
The turnout was reported as 74 percent.
The official results are expected to be announced late Monday or Tuesday.
Van der Bellen used a press conference at Vienna's Hofburg Palace to thank his supporters over Sunday's victory.
"I will be president of all, I am going to move in a position over the parties, I am going to hug everyone without discriminating," he said.
In a letter, President of the European Council Donald Tusk congratulated Van der Bellen for the polls victory. "It is my pleasure to extend my wholehearted congratulations on your election as Federal President of the Republic of Austria."
Wishing Van der Bellen success in his term as president, Tusk added: "At a time when we are faced with many difficult challenges, the continued constructive contribution of Austria to finding common European solutions and keeping our European unity will remain essential."