The Rams were given permission to speak with The Glovers boss last week but Johnson has decided that he wants to remain with the newly promoted League One side.
"I am very appreciative that Derby County showed an interest in me," Johnson told the official Yeovil website.Johnson Turns Down Derby Offer
"I am also very grateful to the Yeovil Town Board of Directors for granting me permission to speak to Derby.
"But after a lot of thought and deliberation I have decided not to take the situation any further.
"Out of respect to the Yeovil Town Board of Directors, the fans, players and my staff I felt this decision needed to be taken now to alleviate any further disruption to our pre-season plans."