The 23-year-old joined the Iron from Heybridge Swifts in August of last year and now leaves to join fellow National League side Aldershot.
As the club announced his departure this evening, Grant posted a message to the club's fans.
"Some things are never easy in football and the decision I have made in regards to my future wasn't easy," he wrote on his Twitter page.
"I would like to thank everyone associated with Braintree Town for all the memories that we created. I thank the management team of the past and the management team that are now present for helping me develop and gain valuable experience and memories.
"I would like to thank each and everyone of the amazing supporters who have supported me from being injured to coming back and having to play reserve games to then that magical moment in the play off final.
"Lastly I would like to thank all my team mates. No one can take away the memories we built and without my team mates all of this wouldn't be possible.
"But now it's time for me to enter a new chapter of my career and in doing so I wish the club nothing but the best for the season and the seasons to come."