He had another year of his contract left to run, but was offered an extension to protect the club's interests in the long term.
Sparrow has formed a strong midfield combination alongside Wayne Graves and Alex Calvo-Garcia, both of these players have committed their futures to the club in recent weeks.
"Matthew is a young player for the immediate future and I am pleased he has agreed the new terms we have offered," said manager Brian Laws today.
This leaves forward Brian Quailey as the only player yet to answer the club on the proposed deal.