Infantino was on Friday elected the new president of FIFA after polling the necessary number of votes in the second round, springing a surprise to outstrip favourite Sheikh Salman bin Ebrahim al-Khalifa.
In his victory speech, Infantino vowed to "restore the image and respect of FIFA", with the organisation still reeling from corruption allegations that have resulted in the arrest of several high-ranking football officials and Blatter being suspended from all football activity for six years.
But Blatter was in magnanimous form about his fellow countryman after the result was confirmed.
He told ZDF: "I'm glad Gianni Infantino is president, a man from the upper Valais such as myself.
"I had gluhwein [mulled wine] with him around Christmas and gave him tips."
Infantino's first term in office will run until 2019.
In a statement, Blatter also backed Infantino as the man to clean up FIFA's tainted image.
"I congratulate Gianni Infantino sincerely and warmly for election as the new president," Blatter said.
"The agreed reform package means the demands on him are high because the implementations of the new structures will be a major challenge. But I am convinced that my successor is ready to meet this.
"With his experience, expertise, strategic and diplomatic skills he has all the qualities to continue my work and stabilise FIFA once more. I wish him good luck and success."
