The 30-year-old centre-back joined Porto from Corinthians in 2016 and swiftly established himself as a key player, featuring 93 times in the Primeira Liga in his three years.
A Brazil international, Felipe has been linked with a move away from the club for the last few months.
He had been widely tipped to join Atletico as Diego Godin's replacement, with the Uruguayan's exit already confirmed.
Although Felipe did not reveal his next destination on Monday, he did send a parting message to Porto fans.
Writing on his official Instagram account, he said: "It was three years of living intensely blue and white with a new family that I built, and that will be remembered for the rest of my life!
Foram 3 anos vivendo intensamente azul e branco com uma nova família que construí e que ficará marcada para o resto da minha vida! Só tenho a agradecer a todos os funcionários do clube, diretoria, presidente, aos místers e companheiros com quem convivi nesse período. Um enorme carinho a todos os adeptos que se manifestam aqui e àqueles que ficam horas esperando na porta do CT ou estádio. Meu muito obrigado pelo reconhecimento e por tudo que fazem por mim! O @fcporto me fez sentir em casa e viver grandes emoções, com conquistas, gols, duelos de Champions League, muita superação e entrega em campo... Virou o clube que mais defendi na minha carreira profissional e pude voltar a ser chamado para Seleção Brasileira e estrear representando meu país. Não há palavras para descrever o quanto aprendi e evoluí como pessoa. Desejo a maior sorte no futuro para os que ficam. Estarei na torcida e serei grato eternamente! Obrigado Malta! #F28 #CarinhoEnorme #FCP #MuitoGrato
"I just have to thank all the staff of the club, the board, the president, the coaches and team-mates with whom I lived in this period.
"I have a great affection for all the fans who are here and those who wait for hours at the door of the training ground or stadium. My thanks for the recognition and for everything you do for me!
"Porto made me feel at home and live great emotions, with achievements, goals, the Champions League, a lot of overcoming and delivering on the field.
"It became the club that I represented the most in my professional career and I was able to return to be called to the Brazilian national team and debut representing my country. There are no words to describe how much I have learned and evolved as a person.
"I wish the best of luck in the future for those who stay. I'll be in the crowd and I'll be forever grateful! Thank you!"
And Porto have now confirmed the defender's departure to Atleti in a statement on Tuesday.
It read: "Porto hereby informs the market that it has reached an agreement with Atletico de Madrid for the definitive transfer of the sports registration rights of the professional soccer player Felipe for the value of €20,000,000."