Sarll has been at the Glovers since 2019 and leaves the club 12th in the Vanarama National League after three successive wins.
His new club Woking have been without a manager since the departure of Alan Dowson earlier this month.
Ian Dyer had been in temporary charge of the Cards - he will revert to his role as assistant manager as Sarll looks to 'close the gap' on the top sides.
"I am very honoured and proud to be offered the manager's position at one of the last great Non-League institutions," Sarll said in a statement on Woking's website.
"For years Woking has found success at the very top of Non-League, and in tandem with John, Drew and the Board, my ambition is to close that gap that exists right now within what is a very competitive division.
"After twenty years of working in this industry, I hope my experiences can accelerate the professional on-field growth of the Football Club.
"I am looking forward to meeting the players and staff and all of you – the supporters."
Sarll's first game in the dugout will be a trip to Boreham Wood - a game that will be live on BT Sport on Saturday.
Charlie Lee will take temporary charge at Yeovil Town, the club announced.