The 36-year-old, who played nine times for England, has made the switch to the National League South side on a three-year deal. Dagenham announced earlier on Saturday that they had been taken over by a Qatari consortium.
Carroll left Bordeaux last month following one season in the fourth tier of French football.
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Speaking on Sky Sports, he said: “The level doesn’t matter as long as I get on the pitch and play football.
“I have had clubs ringing me up, higher leagues, but it has to be the right fit and I need to be in control of what I want to do and not go somewhere because it is higher or there is more money involved.
“I know what will suit me and this is something I believe can be fantastic. There is a project in place, getting them back out of non-league and up the leagues. It is just a great place to be.”
As well as playing for Newcastle and Liverpool, Carroll has had spells with West Ham, Reading and West Brom and spent the last two seasons in France, first with Amiens and then Bordeaux.
He continued: “I have more excitement now than I ever have. I just love playing football and showing everyone I am playing for the love of football, rather than the money or level. It is something I want to do and I am lucky that I can continue to do that.”