The 51-year-old Slovenian lawyer was the only candidate going forward for election at the UEFA Congress in Rome.
UEFA has warned clubs thinking about leaving the Champions League that they would "no longer be great" but praised the FIGC for its handling of racism.
FIFA President Gianni Infantino, meanwhile, said a task force set up to look at possible formats for the competitions may not complete its report by March as originally scheduled.
UEFA president Aleksander Ceferin told Europe's top managers they have "no excuses" for moaning about video assistant referees (VAR) anymore after only five of them came to a special briefing on the subject this week.
Ceferin says letters UEFA received from former lawmakers and NGOs in Ukraine were "without any concrete proof" or evidence of ongoing court proceedings.
Ceferin took over two and a half years ago after the corruption scandal that toppled his predecessor, Frenchman Michel Platini.
Ceferin was president of the Football Association of Slovenia between 2011 and 2016, and had been the President of UEFA since September 14, 2016.
"European clubs are financially healthier than ever, the problem of debt has been sorted out in many countries, and unpaid debts owed to clubs, coaches and players seem to be becoming nothing more than a bad memory".
European football's governing body have since launched their own investigation into the allegations and there is a possibility that the Premier League champions could be hit with a sporting sanction, such as a ban from the Champions League.
- England retained the FIFA vice presidency reserved for the four British soccer federations. "I am the president of UEFA, a UEFA that can be proud of its past and confident about the future", said Ceferin. The only thing great about you would be your past.
World Cup, held every four years, and a global version of UEFA's Nations League.
"Thank you once again for placing your trust in me", Ceferin said after the vote was announced.