The nationalist won the largely ceremonial presidency by edging liberal incumbent Ivo Josipovic in a run-off vote in January amid deep discontent over economic woes in Croatia.
The inauguration ceremony of Grabar-Kitarovic, a former foreign minister, ambassador to Washington and an ex-assistant to the Nato secretary general, was attended by thousands of cheering supporters at a square in the old part of the capital, Zagreb.
Dozens of regional leaders and foreign officials attended the event.
After taking her oath, Ms Grabar-Kitarovic said she will work on making Croatia -–which has a 20 per cent unemployment rate and a six-year recession -–“a rich state” .
She said that after Croatia joined the EU in 2013, “I wish we start living the lives of people in the European Union.”
During her election campaign she used tough words about neighbouring Serbia, Croatia’s foe during the war for independence in the 1990s. But yesterday she called for resolving the differences and said all neighbours should join the EU for the sake of lasting peace in southeastern Europe.
“We are seeking for a better life in the future, without looking to the past,” she said.
SCOTSMAN TABLET AND MOBILE APPS
The victory for Grabar-Kitarovic – giving her a five-year term – boosts the chances of her centre-right Croatian Democratic Union regaining power in elections due this year.
Grabar-Kitarovic, 46, is the fourth Croatian president since independence from the former Yugoslavia. Autocratic nationalist president Franjo Tudjman and his conservative HDZ party ruled Croatia until his death in 1999, marking the start of democratisation that put Croatia on track to the EU.
Ms Grabar-Kitarovic won the January elections by the narrowest of margins.
She secured 50.5 per cent of the vote while incumbent Ivo Josipovic was on 49.5 per cent
The election was seen as a key test for the main parties ahead of parliamentary elections expected to be held towards the end of 2015.
Ms Grabar-Kitarovic is a politically conservative member of the Croatian Democratic Union (HDZ), which pushed the country towards independence from the former Yugoslavia in 1991.
The 46-year-old is a former foreign minister and assistant to the Nato secretary general.
“I will not let anyone tell me that Croatia will not be prosperous and wealthy,” she told jubilant supporters in the capital Zagreb, calling for national unity to tackle the economic crisis.
Mr Josipovic, a 57-year-old law expert and classical composer, had been president since 2010. He had been so popular for so long that it seemed impossible he could fail in a bid for re-election.
Political commentators said his problem was that he was backed by the governing, centre-left coalition that has failed to pull Croatia out of a six-year-long recession.
Prime Minister Zoran Milanovic apologised for being a “burden” to the outgoing president
Croatia, which became the newest member of the European Union when it joined in July 2013, has an unemployment rate close to 20 per cent.
The Croatian president has a say in foreign policy and is head of the army, but running the country is primarily left to the government.
Mr Josipovic proposed constitutional changes to solve the economic crisis.