Ward, who began his second spell as Rovers boss in 2012, steered the club to a mid-table finish last term but has struggled to find consistency this campaign.
Clarke became Rovers' assistant manager in the summer and the former Salisbury player-manager now faces the task of keeping the Pirates, who sit 20th in the Sky Bet League Two table, in the Football League.
Rovers chairman Nick Higgs told the club's official website: "This is something we have had planned for a while, with discussions taking place as far back as last season.
"We believe this is now the right time to make the switch, as we have to plan for next season and try to progress the club forward.
"This gives Darrell time to prepare for the pre-season and think about recruitment for next season.
"Darrell is an enthusiastic and ambitious young man, and he wants to achieve success here.
"We are 100 per cent behind him in his new role, and are confident that he and John will continue to work extremely well together."
- Sports & Recreation