Late on January 12, a US defense official said plans were in place for Iran to return the sailors to a US Navy vessel in international waters early on January 13.
Both US and Iranian officials described the sailors, whose boats may have inadvertently drifted into Iranian waters, as safe and well-treated. US defense officials said nine men and one woman were aboard the two vessels seized.
White House spokesman Josh Earnest told CNN that "We have received assurances from the Iranians that our sailors are safe and that they will be allowed to continue their journey promptly."
Official Iranian news outlets confirmed the detention of the 10 Americans, hours before US President Barack Obama was due to make his final State of the Union address to the US Congress before he leaves office in January 2017.
"The Revolutionary Guards naval forces seized the American boats two kilometers inside Iranian territorial waters while they were snooping around," Iran's semi-official Fars news agency said.
Officials from Iran and the United States were negotiating to free the crew, Fars reported.
Washington and Tehran, which have pursued a partial detente in recent years, both appeared eager not to let the incident escalate further.
Obama, a Democrat, has made the Iran nuclear accord a centerpiece of his foreign policy, and Republicans vying to succeed him have assailed him over the deal.
Iran, meanwhile, is eager for relief from punishing economic sanctions under the landmark nuclear accord it forged with six world powers last July. Formal implementation of the accord could begin in days, following steps Iran agreed to take to curb its nuclear activities.