The 38-year-old has been in interim charge since Andy Hessenthaler left for Dover last month.
Performances in the draw with title chasing Leyton Orient and Salford City in the past week have convinced the board that they need not look elsewhere.
Strevens revealed that he was told before the game with the Ammies that he had the job.
He told the club’s website: “After hearing the news on Friday, I can’t wait to get started now, I’m really looking forward to the job, it’ll be a hard job but I’m really looking forward to it.
“My first two games in caretaker charge I’ll be the first to admit I wasn’t happy with the performances or the results but the boys have responded with their performances away at Halifax and then two real good results against two real good sides.
“Really, it’s the boys who got me this job and opportunity, I just want to carry on the good work and keep improving.”
Chief Executive Kenny Amor said: “Ben is an ambitious, young manager and is open to new ideas.
“As a board we are fully behind Ben, we will be investing in the coaching and support network he has at his disposal to ensure he has the correct resources to do the job. His assistant manager will be announced later this week.”