He takes the role at the Ryman League Division One South club with immediate effect and he will be succeeded by Mark Beard, who has been promoted from Albion's academy staff to assist Ian Buckman.
Hinshelwood, who played for Albion between 2002 and 2009, making 100 league appearances, returned to the club as assistant to under-18 coach Ian Buckman in the summer of 2015 from Worthing.
The 33-year-old was in charge at Woodside Road for two years and was also manager of Selsey in the County League, after a knee injury forced him to retire from the professional game as a player in 2010.
Brighton academy manager John Morling said: "We are very sorry to lose Adam, as he is an excellent young coach, but we understand this is a great opportunity for him.
"He wants to be a manager, and has been a number one previously with Worthing and Selsey, and at Hastings he will have the chance to further develop his career.
"The job will also allow him more time with his young family, and for footballing and family reasons, we understand Adam's motivation for wanting to take the job.
"On behalf of all at the club, I'd like to thank him for his efforts during his two years with us, he's been a pleasure to work alongside, and we wish him well in his new role.
"I'd also like to congratulate Mark on his new position. He's another superb young coach, who has demonstrated great ability during his time here, and I believe he will provide a seamless continuity when stepping up to assist Ian."
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