The Scotland under 21 international will be a free agent at the end of June but City will have to pay a nominal compensation fee because the player is less than 23 years old.
"I am delighted that Gareth has agreed to join us. He has got a good calibre and is at the right age. He can only get better as a player," Foxes boss Micky Adams told the clubs official website.
"We hope to agree a fee with Nottingham Forest but we are prepared to go to a tribunal if necessary.
"Gareth is the first of a number of players that we hope to bring in over the summer."