The 28-year-old midfielder, son of City boss Gary Johnson, has moved to Pride Park on an initial one month loan deal.
City have given The Rams authorisation for Johnson to play in their FA Cup Third Round tie against Millwall this weekend.
"Lee is a terrific player and gives us some much needed cover in the midfield positions," Rams manager Nigel Clough told the official Derby County website.
"We are grateful to Bristol City for allowing him to come and also allowing him to feature in the FA Cup tie; he will certainly be in the squad.
"We have lost a few players with some of our other loans expiring, as well as a number of suspensions and injuries, so it's vital to get some fresh faces in quickly.
"Lee is a very good footballer, who knows the game inside out, is experienced at this level, versatile and works extremely hard for the team; these are the qualities we are looking for."