Carroll, formerly of Newcastle and Liverpool, has left Bordeaux to join Daggers, which currently play in the National League South.
The Geordie has penned a three-year contract and also taken a minority stake in the club. Carroll's deal came just hours after it was announced Daggers had been bought by a Qatari consortium
Dagenham were purchased by a consortium of Qatari private investors on Saturday morning.
Youseph Al Sharif was named interim chairman, with former captain Anwar Uddin coming in as non-executive director.
Carroll as shareholder
On his role as shareholder, Carroll told The Sun: "I didn't want to finish playing football and I'm really excited to get involved in the leadership side and be a player. I've got experience in seeing how clubs are run, of all levels. I think I can add value.
"My first job is to go in as a player, I want to get them promoted. I was offered clubs with a lot more money, but I realised Dagenham was a project that I really wanted to get into.
"I was getting offers from clubs in France, Italy and Spain, but I wanted to come home. I could sign for a top club, but me and the managers might not see eye to eye, so I just want to be somewhere I'm going to be happy."