The Trump administration said Friday it will renew mining leases to extract copper and nickel adjacent to a Minnesota wilderness area, reversing an Obama administration decision and giving a victory to a Chilean billionaire who is renting a mansion to the family of the president’s elder daughter.

The Democratic administration of former President Barack Obama in its waning days blocked a plan by a company controlled by the family of Andrónico Luksic to build a giant copper-and-nickel mine adjacent to a Minnesota wilderness...