The Liverpudlian has signed a two-year contract with the Gills and joins defender Alex Lacey at Priestfield.
Eaves scored seven goals in all competitions for Town after joining last summer.
Everyone at the club would like to wish Tom all the best for the future.
I would like to thank everyone involved at @YTFC from the staff, players and the fans for your support. Good luck for the upcoming season!
— Thomas Eaves (@Thomas__Eaves) June 22, 2017