Reading director of football Nick Hammond said: "Stephen Hunt has been a very effective player in the four years he has been at Reading Football Club, and given us great value.
"He developed enormously as a player here, coming to us on a free transfer and going on to become an established international player.
"He has made it known for some time that he was ready for a new challenge, and this is a good move for all three parties.
"We wish him all the very best for the future."
Hunt is set to make his debut against Chelsea on the weekend.