"This invitation reflects the long-standing historical friendship and alliance between our countries and the strength of relations between the two presidents," Macron's office said late Monday.
The invitation was reportedly made at the insistence of Trump's wife, Melania.
Macron hosted the couple in Paris on 13-14 July last year, treating them to a dinner on the Eiffel Tower and a seat at the Bastille Day military parade, which impressed the US leader so much that he has said he wants to organise a similar show of armed might in Washington.
The programme of Macron's visit has yet to be finalised but it will include a meeting between the presidents, a joint press conference and a state dinner.
Macron may also visit New Orleans, which this year celebrates the 300th anniversary of its founding by the French in 1718, according to diplomatic sources.
The two presidents say they have friendly relations, although they disagree on several questions, notably Trump's decision to pull the US out of the 2015 Paris climate change accord.