The children, aged nine and 12, were digging a hole on Nørre Vorupør beach in North Jutland on Sunday when the dune collapsed, burying them.
The Central Jutland health authority said the boys died on Tuesday evening.
Police said that they considered the incident a "tragic accident" and also said that the boys' families had asked to express their gratitude for the support and help they have received from emergency services and the local community.
Media reports said the boys, who were on holiday with their families from the Munich area, were trapped under the sand for up to 40 minutes during efforts to dig them out. They were given cardiopulmonary resuscitation on the beach and then flown by helicopter to Aarhus University Hospital.
In a separate incident on Sunday, another young boy was caught in a dune landslide in southwestern Jutland, but he was pulled out quickly and unharmed.
Following the incidents, Danish authorities urged people to exercise caution around dune areas on the west coast as recent heavy rains had made the dunes unstable.
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