Burns has spent the past four seasons on loan at Swansea, Stevenage and most recently Hull where he played 11 games last season. He also boasts one senior appearance for City.
Royals manager Noel Hunt said of Burns: "His attitude is second to none and comes from a great calibre of an academy at City and has grown in stature but getting appearances in the Championship last season.
"In the games he played he carried himself very well, and we're really positive."
Reading CEO, Joe Jacobson, also said: "Finley signing on loan is a real coup for the Football Club, we're delighted to have secured his signature against stiff competition.
"We'd like to thank Manchester City for trusting us and our Coaching Team to develop and improve their player, and hopefully this will be the start of a fruitful relationship between the clubs."