Felipe VI has called for “a new Spain that we will build together” after being proclaimed the country’s head of state in a ceremony in parliament.
Earlier, King Felipe received the royal sash from his father, Juan Carlos, at the Zarzuela Palace near Madrid.
He acceded to the throne at the stroke of midnight after Juan Carlos formally abdicated on Wednesday.
Correspondents say the proceedings have been kept low key, with many Spaniards suffering economic hardship.
The swearing-in ceremony took the form of a proclamation rather than a coronation. It is the first royal transition in Spain since democracy was restored in the 1970s.
The new king, 46, swore an oath promising to uphold the constitution.
The speaker of the lower house of parliament, Jesus Posada, then proclaimed him king, declaring: “Long live Spain! Long live the king!”
In a speech to parliament, Felipe said he had “great hope” for the future of Spain and called for unity.