Songo'o, City's eighth capture of the Adams' era, had been widely expected to link up with the Scotsman again after recently announcing that he was ready for the "next chapter" after leaving Morecambe following their historic promotion to League One
The 29-year-old Frenchman, who has signed a two-year contract, has also previously played under Adams at Plymouth Argyle and Ross County.
Songo’o said: “I am delighted to have got the deal done. When I got the call from the gaffer, I felt it would be a huge assignment for me at a historic club.
“I am keen to be a part of the project the gaffer is building and was desperate to come in as soon as possible, so am really pleased to be here.
“The gaffer has always found a way to get the best out of me, and has helped me progress wherever I have been with him.
“This is a club which speaks for itself, and it did not have to be sold to me too much. I am excited for what is ahead and hopefully helping us achieve our aim - which is, this season, undoubtedly promotion.”
Adams added: “I am delighted to have been able to bring Yann here with us, as a player I know so well and have a huge amount of trust in.
“Having worked with him at three other clubs, I have no doubts over not only the character we are bringing in, but also what Yann will add on the field for us.
“He is a battler and a winner with real resilience - and physical and mental strength. Yann will give his all on the field for his team-mates and supporters, and typifies the kind of values needed to play for Bradford City
“I have a feeling our supporters will enjoy watching Yann put his body on the line for three points over the next two years and beyond, and I am looking forward to working with him once again.”
Songo'o joins fellow newcomers Alex Gilliead, Andy Cook, Abo Eisa, Lee Angol, Oscar Threlkeld, Liam Ridehalgh and Fiacre Kelleher at the club.