The exhumation followed a court order on behalf of a woman who says her mother had an affair with the painter.
If she is proved right, she could assume part of the Dalí's estate, currently owned by the Spanish state.
It may take weeks before the results of the tests are known.
The surrealist painter, who died in 1989 at the age of 85, was buried in a crypt in a museum dedicated to his life and work in Figueres, in north-eastern Spain.
A crowd gathered outside the museum to watch as police escorted the experts into the building on Thursday evening.
The exhumation went ahead despite the objections of the local authorities and the foundation carrying Dalí's name, both of which claimed that not enough notice had been given ahead of the exhumation.
María Pilar Abel Martínez, a tarot card reader who was born in 1956, says her mother had an affair with Dalí during the year before her birth.
Her mother, Antonia, had worked for a family that spent time in Cadaqués, near the painter's home.
Last month a Madrid judge ordered the exhumation to settle the claim. It is contested by the Dalí foundation, which manages the estate of the artist, who was not believed to have had any children.
Her action is against the Spanish state, to which Dalí left his estate.
Ms Martínez says her mother and paternal grandmother both told her at an early age that Dalí was her real father.
But the claim has surprised many, including Ian Gibson, an Irish-born biographer of Dalí, who said that the notion of the artist having an affair that produced a child was "absolutely impossible".
"Dalí always boasted: 'I'm impotent, you've got to be impotent to be a great painter'," the biographer said.
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