Spaniard Tena, 26, joined Accies from Livingston in 2013 but has not played since suffering a knee injury against Ayr United in July.
Seaborne signed from Partick Thistle in August but only made 13 appearances.
"We thank both players for their service and wish them well for the future," a club statement said.
Hamilton Academical have released defenders Jesus Garcia Tena and Dan Seaborne "in order to allow them to find new clubs ahead of next season".