Talks over a move back to Argentina began in December, with the former Southampton striker having made just seven appearances in the Portuguese top flight for Porto during the 2015-16 season.
Osvaldo spent part of last year on a loan deal at La Bombonera and he has now sealed a permanent switch after his contract at the Estadio do Dragao was rescinded.
"It feels like I never left. I'm very happy, I'm enjoying the work and my head is focused on working," he said at a media conference.
"I knew there would be a second period at Boca and I thank God that it's come. My last one was good and I think this will be much better."
Osvaldo added his excitement of playing alongside club icon Carlos Tevez in the Boca attack.
He said: "It's a huge joy to play with Carlos, as it is for anyone who plays with him, and even more as it's at Boca."
President Daniel Angelici confirmed that the striker, who turns 30 next week, can secure an extension to his contract should both parties agree.
"Today I have the joy of having Daniel Osvaldo with us again, a big fan of our club," he said.
"We are very happy to have him with us again. In principle, the contract is for 18 months, but it can be extended.
"This type of signing is always easier when the player wants to wear our shirt and Daniel is a great professional who has come back for glory.
"We hope to give joy to the fans by winning the 2016 Copa Libertadores."