The Bowers Museum in Santa Ana, California sent them back after signing a non-prosecution agreement with the US district attorney, Thairath newspaper reported online.
US authorities found that the pots were smuggled from a UNESCO heritage archaeological site in Udon Thani, around 600 kilometres north-east of Bangkok.
The small, earthenware pots, in a variety of conditions, had arrived back in the country and were undergoing inspection for authenticity, the report said.
"Ban Chiang artifacts are very unique so the inspection will not take long," said Anek Seehamatra, director general of the government's Department of Fine Arts.
DPA