Shortly after the result of the vote was announced, Ceferin told the delegates at the extraordinary UEFA Congress in Athens that he was proud to be their new president.
"It's a great honor but at the same time a great responsibility," Ceferin said after the decision was announced by acting President Angel Maria Villar, who had also been a candidate before withdrawing from the race last week.
"My small and beautiful Slovenia is very proud about it and I hope that one day you will also be very proud about it."
Van Praag stressed that the two men were competitors, not enemies, and called on all of UEFA's national associations to throw their support behind Ceferin, who will complete Michel Platini's third four-year term, which expires in March 2019.
"Alex and myself have the same goal, look at our programs," van Praag said. "He wanted to do it his way and I wanted to do it my way and today democracy has spoken."
Who is Aleksander Ceferin?
Earlier, Platini who was granted special permission by FIFA to address the Congress insisted that he had done nothing wrong.
"You are going to continue this wonderful mission without me," Platini said. "I have a clear conscience, I have not made mistakes and will continue my fight in court."
The 61-year-old Platini stepped down as UEFA president in May after the Court of Arbitration for Sport (CAS) rejected his appeal against his six-year ban from all football-related activities, handed down by FIFA last December. However, the CAS did reduce his ban to four years.
FIFA banned Platini over a disloyal payment of some 2 million Swiss francs (1.8 million euros, $2 million), which he received from then-FIFA President Joseph Blatter in 2011 for consulting work done a decade earlier. Blatter was handed a similar ban.