King, 31, made five substitute appearances for the Ibrox club during the first half of the season.
He came on in League Cup games against East Fife and Livingston, the Europa League win over Feyenoord and Premiership matches against St Mirren and Livingston.
Rangers won all five but King's role was limited and he returned to Leicester during the winter break.
The Wales international is in contention to make his Huddersfield debut in Saturday's home game against Brentford in the Championship.
Huddersfield manager Danny Cowley said: "I'd like to begin by giving our thanks to Brendan Rodgers and Jon Rudkin at Leicester City for making Andy's loan possible.
"They've gone out of their way to help a player who has done brilliantly for them, which says a lot both about their club and the player.
"There's a real alignment with what we're striving to do and Andy's goals for the rest of the season.
"We're fighting to maintain our position in the league and Andy is incredibly determined to do well, as he's out of contract soon and fighting to make the Wales squad for the upcoming European Championships."
King has made over 350 appearances for Leicester and played a key role in their Premier League title success in 2016.