The 46-year-old conservative former foreign minister and NATO official narrowly defeated her left-wing predecessor Ivo Josipovic in an election run-off in January.
The leading member of the main opposition HDZ party will serve a five-year term.
"I will be a top economic diplomat of our country," she said in her inaugural speech.
She pledged to do her utmost "to make Croatia a wealthy nation."
"I want that after almost two years of (EU) membership, we all eventually start to live the life of a European Union member," Grabar-Kitarovic said.
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The Croatian economy, hit by a six-year recession, remains among the weakest in the 28-nation bloc. Unemployment is almost 20 percent and the government forecasts a meagre 0.5 percent growth this year.
Grabar-Kitarovic gave her speech immediately after the swearing-in ceremony at Saint Marc's square in the old quarter of Zagreb.
Apart from hundreds of Croatians and top local officials the inauguration was also attended by the presidents of Albania, Bosnia-Hercegovina, Hungary, Kosovo, Macedonia, Montenegro, Slovakia and Slovenia.
Serbia's Prime Minister Aleksandar Vucic was also present.
Grabar-Kitarovic is the former Yugoslav republic's fourth president since its independence in 1991.