The 37-year-old, who began his career at Portsmouth in 1994 and has played for 15 different clubs, has not ruled out a third successive promotion having helped Gillingham to the League Two title in 2013.
"Well, never say never. Anything is possible," the Jamaican told the club's official website.
"There was interest from elsewhere but I've started something here with the lads and I saw the others re-sign and I thought why not carry it on?
"I've been very happy here and with how Russ has been with me, and I thought it was only fair to stay on."
Burton scored six goals in 33 appearances as the Iron secured automatic promotion last season.