Amat arrived from Espanyol on a four-year deal in 2013 and has made 48 appearances for Swansea, agreeing an extension to 2018 in March last year.
The Spaniard has once again extended his stay by a year despite recent managerial changes at the Welsh club following Francesco Guidolin's appointment as head coach for the remainder of 2015-16.
The Italian took over from interim boss Alan Curtis this month following Garry Monk's departure in December.
Chievo striker Alberto Paloschi arrived on Friday as Guidolin's first senior signing, while 21-year-old forward Kenji Gorre has been recalled from his season-long loan spell with Eredivisie side ADO Den Haag.
"After seeing his game-time limited, both parties agreed it was in the best interest of the player to return to the Liberty," Swansea said in a statement.