Sulyok, previously head of Hungary's Constitutional Court, was nominated as President by Hungary's ruling Fidesz party.
He was inaugurated on Sunday in a ceremony in front of Sandor Palace in Budapest.
During he speech he said, "My task and service from now on are different from what I have done before, but the core values remain the same as those to which I have always adhered firmly and faithfully."
"As President of the Republic, the Fundamental Law is the cornerstone, framework, and measure of my work.''
Hungary's previous president Katalin Novak stepped down in February following public outcry after she pardoned a man who had been convicted as an accomplice in a child sexual abuse case.
The controversial decision caused mass protests and threatened the power of Hungary's ruling Viktor Orban.
“The year 2024 could not have started in a worse way. Our President of the Republic has submitted her resignation to Parliament. This is like a nightmare, and it is taking a toll on us all,” the Hungarian premier said in his State of the Union address in February. “We must submit to the National Assembly a new legislative package on child protection.''
Sulyok has been a judge of the Constitutional Court since 2014. Following his election as Hungary's new head of state he promised transparency in his decisions.
Despite having the backing of the ruling party, the opposition has criticised Sulyok for having little political experience. A protest orchestrated by four opposition parties on the Sunday of his inauguration called for direct presidential elections.
The role of president in Hungary is largely ceremonial, though they do have the power to send bills back to lawmakers or to the Constitutional Court for review.
