The winger has put pen to paper on a three-year deal at Pride Park, keeping him at the club until the summer of 2021.
"Florian is a player that I have been tracking since I first got the job here so it's fantastic for us to get the deal done," Lampard told the club's official website.
"I watched him at Brentford last season and he is an exciting player. He is willing to run at and in behind defenders so his speed and creativity make him another really strong addition to our squad. At 27 I think he's in a prime age and I am sure he can bring all his excellent qualities to Derby County.
"Credit should go to the club for getting this deal, and the Mason Mount and Harry Wilson signings, over the line this week. They are all players that I seriously wanted so I certainly appreciate the hard work that has gone into these transfers. I believe we are putting together a side that can be exciting and really compete in the Championship."
Jozefzoon, who could make his first appearance for the club during their pre-season friendly against Southampton on Saturday, scored eight goals in 62 appearances for Brentford during his one-and-a-half years at Griffin Park.