Songo’o, 29, City’s eighth capture of the Adams era, latterly worked with the Scot at Morecambe, having also been a player under him at Plymouth Argyle and Ross County.
On the midfield enforcer, who has signed a two-year deal, Adams said: “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.
“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.”
A glowing reference from Jon Stead helped Harrogate Town to make experienced former Sheffield Wednesday and Bradford centre-back Rory McArdle their fourth signing of the summer.
The Northern Ireland international has made over 400 Football League appearances in a career which has also taken in Rochdale, Aberdeen, Scunthorpe United and Exeter City.
But his time playing alongside Stead at Valley Parade was decisive in the move, with the striker selling Harrogate to him.
McArdle said: “He said nothing but good things. Character-wise, I think I’m quite similar to Steady, so for him to have enjoyed it as much as he did, it’s something I’d like to think I’m going to be able to enjoy as well.
“If I can be half as successful as what Steady was when he was here, then it’s something I’d be happy with.”