The 27-year-old is expected to complete his medical in Spain before finalising a move that will end his successful spell in Portugal.
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According to Fabrizio Romano, Atletico will pay €40 million upfront for the midfielder, with a further €5 million possible through add-ons.
Hjulmand leaves Sporting after 141 appearances, 10 goals and 12 assists, helping the club win two league titles and a Taca de Portugal.
The Danish captain will sign a long-term contract with Atletico until June 2031 after completing his farewell commitments in Lisbon.