"By ensuring a precedent of transfer of power through parliamentary and presidential elections, we succeeded in moving to a substantially new stage in the development of our state," Margvelashvili, 44, said in his inaugural address.
He pledged to work toward the country's integration with Europe and to improve relations with Russia, the New York Times reported.
"Despite the difficult situation we are facing today, and in parallel with integrating into European and Euro-Atlantic structures, we reiterate our commitment to further dialogue with Russia and build confidence to solve the problems existing today," he said.
Prime Minister Bidzina Ivanisvili, who plans to resign, picked Margvelashvili for the role.
The departing president, Mikheil Saakashvili, did not attend the inauguration.