Several hundred well-wishers, some dressed in period costume, turned out to see the arrival of the three-masted tall vessel with its 80 crew members.
French Ecology Minister Ségolène Royal handed Virginia Governor Terry McAuliffe an engraving of France's 1789 Declaration of the Rights of Man and of the Citizen, which was partly inspired by America's Declaration of Independence in 1776.
Lafayette, who was born in 1757 to a noble family in south-central France, joined the American revolution at age 19, inspired by the cause.
As well as the French troops who joined the American rebels in the month-long battle against the British at Yorktown in late 1781, French ships helped blockade Yorktown port, leading to the British surrender.
RFI correspondent Philip Crowther went to Yorktown and met several of the sailors who volunteered for the 6,000-kilometre journey which left Ile d'Aix on France's west coast.
21-year-old French sailor Benjamin lamented that, although he had a fantastic trip, it was disappointing to see so much plastic rubbish floating in the middle of the Atlantic.
The replica project cost 25 million euros, financed by more than four million visitors to the shipyard in Rochefort in south-western France where the Hermione was built, as well as through crowd-funding initiatives for specific parts of the ship.
Francophiles, historians and tall-ship fans are expected for three days of festivities in Yorktown, which is located near the mouth of the Chesapeake Bay.
The Hermione will be feted as it makes 11 stops on the US east Coast over the next month, including in Philadelphia and Boston. It will also visit Canada.