The decision has been taken after the 55-year-old had overseen a run of form in which Rovers have suffered seven defeats in eight Conference Premier encounters.
"Football is a results driven business and recently results haven't been good enough. I feel I have left the club, both on and off the field, in the best shape it has ever been," Hockaday said in a statement.
"I am proud of what I've achieved here and feel the time is right to move on. I wish everyone at the club the very best. Forest Green Rovers will always have a place in my heart."
Meanwhile, chairman Dale Vince added: "A lot of the changes David has wrought are not as readily visible as a scoreline and are less immediate in their impact - but they are vital to the long term success of the club. David has been a key player in the transformation of Forest Green and I wish him all the very best in his next role."
Former Blackpool and Swindon Town right-back Hockaday originally took charge at The New Lawn in 2009.