Clarke, 35, becomes John Ward's right-hand man at the Memorial Stadium despite having never worked together previously.
Clarke joined Salisbury as a player in 2007 following a lengthy career with Mansfield and Hartlepool, before then becoming player/manager in 2010.
During his three years in charge Clarke has guided the Wiltshire outfit to two play-off promotions, taking the club from the Southern League Premier Division to the Blue Square Bet Premier, as well as the third round of the FA Cup for the first time in their history.
Ward told Rovers' official website: "Darrell has achieved success on a relatively small budget over the last couple of years and has experience as a first-team manager.
"I have never worked with him before, which is exciting for me as he is going to push me as well as himself.
"He has had experience playing at this level with Mansfield and Hartlepool so that will be beneficial.
"He is young, with lots of ambition, but he also brings with him plenty of experience. I look forward to working with him."