The 36-year-old signed a three-year deal with the National League side after leaving Bordeaux last month.
Carroll, who also played for Reading and WBA, scored 54 goals in 248 Premier League appearances and won nine England caps from 2010 and 2012.
He joins the Daggers on the day they were acquired by a consortium of Qatari private investors.
The striker has reportedly taken a minority share in the team.
In an interview with Sky Sports News, Carroll said that he had "clubs ringing me up from higher leagues" but wanted to be closer to his children and chose a team that was "the right fit".
"It doesn't matter the level, or anything, as long as I get on the pitch and play football, that's all that matters," said Carroll.
"Coming here and showing people I am just playing for the love of football rather than the money and the level is something I wanted to do.
"This is something which could be fantastic. We have a project to get them out of non-league and back up the leagues."