Anslow stepped up from assistant to take over for training on Thursday night after Beckingham, pictured, stood down within hours of his third from bottom side's heavy defeat at Salters Lane.
Former Deal Town and joint Hythe Town manager Anslow takes charge for the first time at the Maidstone Road Sports Ground on Saturday when the Chats host South Park in Ryman South.
Appointed in the summer as the successor to Kevin Horlock, former East Grinstead Town, Phoenix Sports and Hythe Town boss Beckingham departed having won only one of his 11 games at the helm.
Chatham Town
Chatham Town chairman Jeff Talbot confirmed the club's managerial shake-up and looked forward to Anslow lifting them up the table in the Kent Messenger.
He said: "We've not had the best of starts this season - things haven't gone to plan. Tony resigned straight after the game. When you've lost 7-1 there's not much you can do. It's difficult to come back from that. He took it on the chin and resigned.
"Darren's stepping up as manager. He's got the job of picking us up, shaking us off and getting us out of the bottom half of the table. The players are quite happy with his appointment. We've got a game on Saturday and we need three points. It's like Darren said, after a 7-1, it's got to be up from here."
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