The 24-year-old has agreed personal terms on a two-and-a-half year contract at Filbert Street and will be officially unveiled by The Foxes on Friday.
The former England Under-21 international has joined Dave Bassett for the second time in his career, after he signed for him when he was Forest boss.
"Alan is a very talented lad who I am delighted to bring here to Leicester," said Bassett.
"I've always admired him as a player and he will give us a lot of options. I brought him to Forest as a left-back but when Ron Atkinson came in he played him in midfield and he excelled there as well.
"Alan's a proven goalscorer, he's got good pace and a good left foot which in this day and age is not easy to find. I think he'll bring good competition to the team because we're not over-blessed with players.
"He had a terrible injury last season but there is no problem now. I've been assured he's fully fit and he's played some football for Forest this season.
"I'm looking forward to working with him again. He's got a lot to offer us."
Leicester are likely to add a second player to their squad before this weekend's clash with Manchester United by concluding a deal for Middlesbrough centre forward Brian Deane.
"We're very close to doing a deal there," said Boro boss Steve McClaren.
"We're just waiting for things to develop between the player and his personal terms."
Meanwhile, Leicester have revealed that they will not be signing French trialist Jocelyn Gourvennec because they do not have enough money, but Bassett insisted that he will be keeping a close eye on the Rennes midfielder.
"I've been very pleased with Jocelyn this week and he's certainly somebody who could give us something," he said.
"Unfortunately I thought we had a bit more cash than we have and I've got to send him home.
"We can't sign him at the moment because financially it's impossible.
"I may well take another look at him later this season. Then again, I may lose him to somebody else because he's looking for a move.
"I've actually apologised to him because a week ago I might have been able to do something but now I can't. He'll certainly be someone we'll consider again."
