Lajcak, 54, was elected by acclamation as President of the 72nd session of the UN General Assembly at a special session here.
The 72nd session of the United Nations General Assembly will commence from September 12.
Lajcak, who was one of the candidates last year for the position of UN Secretary General, will succeed Fijian diplomat Peter Thomson.
"Thank you @UN General Assembly 4 electing me the next @UN_PGA. Looking fwd to work w/all of you to make this world a better place to live in," Lajcak, Slovakia's Minister of Foreign and European Affairs, tweeted following his election.
UN Secretary General Antonio Guterres congratulated Lajcak on his election, saying he has always demonstrated an "impressive command" of all aspects of UN action and a strong commitment to the principles that govern our work.
Lajcak has expressed his firm belief that "strengthening the UN is the best investment to achieve the universal desire for peace, development, equality and justice in the world," the UN chief said.
"I think that both of us saw high expectations and got a strong sense of how much governments and people need the United Nations to respond to the deserving cries of people around the world for lasting peace, justice, human rights and human dignity," Guterres said.
The UN chief thanked Thomson for his leadership over the past year, voicing appreciation for guiding the General Assembly "outstandingly well" during the transition from Secretary-General Ban Ki-moon to Guterres taking charge at the helm of the UN.
"Your very strong commitment to the implementation of Agenda 2030 and the Paris Agreement on Climate change and your enthusiastic leadership in relation to the Oceans Conference represent a legacy that will never be forgotten in the United Nations," Guterres said.
In May last year, the Slovak government had formally nominated Lajcak as a candidate for the position of UN secretary-general.
A career diplomat, Lajcak is a graduate of the Moscow State Institute for International Relations.
At the age of 31, he was appointed Slovak Ambassador to Japan, and later to Yugoslavia, Albania and the Former Yugoslav Republic of Macedonia. In 2009, he became Minister of Foreign Affairs of the Slovak Republic and later, in 2012, the Deputy Prime Minister and Minister of Foreign and European Affairs. In addition, he became Chairman of the Slovak Government's Council for Human Rights, National Minorities and Gender Equality.
In 2007, Lajcak was appointed High Representative of the International Community and EU Special Representative in Bosnia and Herzegovina. During his tenure, Bosnia and Herzegovina signed the Stabilisation and Association Agreement with the EU.
He also launched activities to reach out to the population, including speaking tours and a website for dialogue with citizens.