Midfielder Miguel Pallardo has signed a new one-year deal with newly-promoted Hearts.
Liam Rosenior has thanked the fans of Hull City for "five wonderful years".
The 22-year-old moved to Vicarage Road permanently in the summer of 2013 after a loan spell and has since made over 60 appearances for the Hornets.
Battocchio began his career with Newell's Old Boys in Argentina before signing his first professional contract with Udinese in 2011.
He earned his first call-up to the Italy Under-21 squad last year and has gone on to score two goals in eight appearances.