Huntington signed for an undisclosed fee from Newcastle United yesterday evening and Da Costa's transfer from Ionikos was made shortly before the closure of the transfer window, bringing the number of deadline-day arrivals at Elland Road to three.
United had secured Scottish goalkeeper Alan Martin from Motherwell earlier in the day, providing cover for first-choice keeper Casper Ankergren.
Centre-back Huntington, who will be 20 later this month, made 11 Premiership appearances for the Magpies last season and also played in two UEFA Cup matches. He was not expected to figure prominently under Sam Allardyce at St James' Park this season.
United have also turned to raw potential in Da Costa, a 23-year-old left winger who has signed a one-year deal.