Earlier, King Felipe VI 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 ceremonies have been kept low key, at a time when many in Spain are suffering economic hardship.
The ceremony takes the form of a proclamation rather than a coronation. It is the first royal transition in Spain since democracy was restored in the 1970s.
King Felipe VI, 46, swore an oath promising to uphold the constitution.
Congress President Jesus Posada then proclaimed him king, declaring: “Long live Spain! Long live the king!”
In a speech to parliament, King Felipe thanked his parents and said he had “great hope” for the future of Spain.
“You will find in me a loyal head of state who is ready listen and understand, warn and advise as well as to defend the public interest at all times,” he said.
“The monarch wants to be close to citizens… ensuring it can preserve its prestige and dignity.”
“Now more than ever, citizens of Spain are rightly demanding fundamental ethical principles should govern our public life. The king should not only be a reference but who serves all citizens of Spain.”
No foreign leaders or royal families have been invited to the event.
King Felipe and his wife Letizia will later be driven through Madrid’s streets before appearing on the front balcony of the Royal Palace.
Correspondents say the new king faces a series of tough challenges if he is to restore the reputation of the monarchy.
Although King Juan Carlos won plaudits for his role in restoring democracy, his image suffered when he went on a luxurious African elephant-hunting safari in the midst of a recession.
His reputation suffered further damage because of tax fraud allegations made against his daughter, Infanta Cristina, who is reported not to have been invited to the succession party.
At the same time many Spaniards are demanding a referendum on whether to have a monarchy at all.
A demonstration is scheduled to take place in central Madrid on Thursday, the same day as the enthronement, despite a ban imposed by authorities.
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