Robins manager John Ward said: "Obviously it is disappointing to lose Kay, but the opportunity to play at a higher level was too good for him to turn down and for the club it is another record transfer fee we have received.
"Kay has improved tremendously in the last three years and he deserves the chance to test himself in the Championship.
"We must now move on and the challenge for the forwards that remain at the club is now to step up and fill his shoes by scoring the goals for us."