A White House statement said that Trump will welcome Najib to Washington on September 12 to strengthen ties "with one of America's closest partners in Southeast Asia".
The Malaysian foreign ministry confirmed the visit.
Najib has been battling allegations that billions were looted from a sovereign wealth fund, 1Malaysia Development Berhad (1MDB), in complex overseas deals that are being investigated by authorities in several countries.
Both the prime minister and the fund deny any wrongdoing.
US authorities are trying to seize assets, from high-end real estate to artworks, it says are worth about $1.7 billion.
The lawsuits said a figure called "Malaysian Official 1" knowingly received huge sums of 1MDB money. A Malaysian Cabinet minister has confirmed that official was Najib.
Despite the scandal, the US views Malaysia as a key ally in Asia as it seeks to combat Beijing's growing influence and will be keen to shore up relations.
The Wall Street Journal, which first reported the trip, said Najib has been eager to emphasise his friendship with Trump, and is keen to use the visit to downplay the possibility of further probes.
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