The Brazilian departed Los Rojiblancos on a free transfer this summer after having played 333 games with the LaLiga Santander club.
"Feeling that passes on from father to son, from grandfather to grandson," Filipe Luis posted on social media.
"The big day has arrived; the day to fulfil my dream as a child. The day I can say that I am a Flamengo player."
In his two spells at Atletico he scored 12 goals, assisted another 27 and won seven titles.