The 51-year-old Slovenian lawyer was the only candidate going forward for election at the UEFA Congress in Rome and was voted in by acclamation.
His election was in contrast to the situation when he took over two and a half years ago, with football in turmoil amid a corruption scandal that toppled his predecessor Michel Platini.
Ceferin told UEFA's 55 member associations who elected him unopposed that "with unity restored" he was taking over with "fewer doubts and less scepticism than back then".
"So, what's going to happen now? That is the question many people were asking when I was elected two and a half years ago," said Ceferin.
"At that time, football, at both world and European levels, was being rocked by the most serious governance crisis in its history and yet you decided to entrust the keys to the UEFA house to a virtual unknown."
Having previously been largely charged with putting in place measures voted for under the previous regime of Platini and current FIFA president Gianni Infantino, Ceferin can now hope to really make his mark and implement his own changes.
"We are going to have to think ahead and undertake some major developments," he added.
On top of his agenda for now is a battle with Infantino, who as FIFA president has been promoting a new, expanded Club World Cup and global Nations League. Ceferin is opposed to the projects.
"We must not allow our recent, short-term successes to hide the much more complex challenges that lie ahead," Ceferin warned.
"The most dangerous thing we can do is rest on our laurels and bask in our current situation."
Ceferin promised to work closely with world football's governing body, and is also hoping to bring the 2030 World Cup back to Europe.
"With our unity restored, we will be a source of constructive ideas for FIFA, rather than one of opposition. And we expect the same attitude from FIFA," he said.
'Lost time'
Infantino was present in Rome and also extended an olive branch to his European counterpart.
"We must be innovative. We must continue to develop. It can only be done if we work together, if we discuss, if we debate," he said.
"Let's try to find what we have to do together to make up for lost time."
Previously the head of the Slovenian Football Federation, Ceferin's presidency so far has been less charismatic in his approach than that of Platini.
The Frenchman is still suspended until October this year, when he will complete a four-year ban from all football-related activities following the corruption scandal that also brought down then-FIFA chief Sepp Blatter.
"When crisis hits, it is not the time to suddenly forsake everything that has gone before. I am not the president of a 'new UEFA'. I am the president of UEFA, a UEFA that can be proud of its past and confident about the future," said Ceferin.
He also defended his record since taking over with his most notable achievement being the introduction of term limits for UEFA presidents, to a maximum of three four-year stints.
"Limited terms of office, the publication of salaries, the creation of a Compensation Committee and the inclusion of independent members in a reinforced Governance and Compliance Committee are just a few of the common-sense reforms we have introduced," he said.
"This is only the start. We will be doing more in this area because there remain weaknesses in our system."