Grant, who formerly played for Tooting & Mitcham, joined The Gills last December and made ten appearances for the Kent club, including nine as sub, and scored his first league goal against Rotherham United back in January.
"Ideally we would like to have our manager in place before bringing in new players for next season because these decisions will be solely his to make," said chairman Stewart Till.
"However, that not being the case, we felt that we needed to act quickly to sign Gavin because he is clearly a very promising young player and any delay on our part might have opened the door for another club to move in ahead of us."