The 22-year-old, a Germany Under-21 international, has put pen to paper on a three-year contract at Griffin Park.
Hofmann moved to Kaiserslautern from FC Schalke last summer and scored eight goals in 33 games for the German second-tier side.
Bees boss Marinus Dijkhuizen told the club website: “Philipp is a target man, physically strong, and a good header of the ball. His style of play is similar to mine when I played.
“He is a different type of striker to Andre Gray, so it gives us more tactical options. Philipp is only 22 so can still improve his game.”