The 31-year-old is the club’s third signing of the January window following the additions of Arsenal winger Emile Smith Rowe and Sheffield United defender Richard Stearman.
Town are also being strongly linked with left-back Harry Toffolo, currently at manager Danny Cowley’s former club Lincoln City.
King, part of the Leicester squad who won the Premier League title in 2015-16, will be eligible for selection for Saturday’s home game against Brentford.
On King, Cowley said: “He’s also been a consistent source of goals from central midfield, netting 64 times in domestic football.
“I would like to begin by giving our thanks to Brendan Rodgers and Jon Rudkin at Leicester City for making Andy’s loan possible.
“They have 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 is a real alignment with what we are striving to do and Andy’s goals for the rest of the season.
“We are 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.”