The 25-year-old winger has signed a five-year deal at Vicente Calderon after successfully passing a medical.
Musampa has enjoyed a tremendous season with Malaga and his form attracted the interest of a host of clubs including Deportivo La Coruna, Arsenal and Newcastle.
Malaga have decided to cash-in on him now rather than risk losing him for nothing when his contract expires next year.
Musampa is expected to be the first of many new arrivals at Atletico as they look to sustain a major challenge in La Liga.
