Burgess is a proven goalscorer in the lower leagues, with the Seasiders beating Brighton to his signature.
"Ben is at the stage where, after the injuries he's had, he needs regular first-team football," Tigers boss Phil Parkinson told the Hull Dail Mail.
"But unfortunately, we have been unable to guarantee him that.
"He's been a very important player to Hull City over the years and we wish him all the best for his future."
Scunthorpe had been linked with an approach for the tall striker, with speculation rife during the close season, but a move failed to materialise.