Johnson has revealed he will be staying in charge of the promoted Glovers after steering them to the League Two title last season.
He said: "I appreciate that Derby County showed an interest in me and I am
also very grateful to the Yeovil Town board of directors for granting me permission to talk to Derby.
"After a lot of 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 staff, I thought this decision needed to be taken now to avoid any disruption to our pre-season plans."
Bolton assistant manager Phil Brown is now favourite to succeed George
Burley in the Pride Park hot-seat.