Felipe, 46, legally became king at the stroke of midnight (2200 GMT) as an act of parliament signed by his father came into force, formalising the end of 76-year-old Juan Carlos' 39-year reign.
Earlier, Juan Carlos signed the act of parliament ending his reign with a golden pen at a ceremony in Madrid's Royal Palace, then hugged his son.
The embrace between the elderly king and his heir under the palace's chandeliers marked the first royal succession in Spain's post-Franco history.
Dressed in a dark blue suit and pink tie, Juan Carlos, who uses a cane following repeated hip operations, stood unaided during part of the ceremony, but had to briefly hold Felipe's arm to steady himself.
A band struck up the national anthem as Felipe in a dark suit, his wife and future queen Letizia in a black top and white skirt, and Juan Carlos's wife Queen Sofia, applauded the abdicating king.
Minutes earlier, cannons had fired a salute and shouts of "Long Live the King!" rang out as the royals arrived by car at the old palace in western Madrid.
Juan Carlos is credited with helping guide Spain to democracy after the death of the dictator Francisco Franco, but his popularity was damaged by scandals in recent years.
Juan Carlos outraged Spaniards in 2012 by going on a luxurious African elephant-hunting safari during a recession, while Felipe's 49-year-old sister Cristina risks being put on trial for alleged tax fraud.
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