The left-back has not received many first team chances with the club this season.
And he will now compete at Ipswich in the Championship.
But Leicester do want him back for next season, as Christian Fuchs is departing at the end of the campaign.
"He is a very good player. He's been training with top players at Leicester and he has handled that well.
"He's got a really good left foot and he wanted to be here and that's vital for me. I need players who want to come here and play for this club."
Elder added: "I had a good chat with the gaffer about three weeks ago and he said he wanted me to come down and be a big part of the squad.
"I was really eager to come and get involved."