The agreement had already been unofficially announced by his new teammate Neymar Jr and the club have since ratified it.
Coutinho, 34, had been without a club since leaving Vasco da Gama in February, citing mental burnout.
A move to join one of Vasco's main rivals is expected to trigger more criticism for the ex-Brazil international and he's looked to explain his position over the saga.
"Vasco has always been my home. I was raised at Vasco, played all through the youth ranks, and made it to the senior team. I've always made clear the affection, gratitude, and love I have for the club.
"When the opportunity to rejoin Vasco came up, I still had a year left on my contract in Qatar, where I was earning $10M net. I want to make that clear so people understand.
"I also still had a year left on my contract with Aston Villa. In order to join Vasco, I always made it clear to everyone who works with me: Vasco wouldn't spend a single cent on my transfer. That was my priority.
"I came back with the mindset of becoming a champion with Vasco and perhaps cementing myself as an idol.
"I know many say it was just a few boos, but anyone who was there knows. The entire stadium was insulting me and demanding I leave. That was extremely tough.
"I had to make the hardest decision of my life, which was to prioritise my health. I knew the consequences, but I was completely honest with myself, and at no point did I abandon Vasco."