The former Newcastle and Liverpool striker moved to the Daggers after leaving Bordeaux at the end of last season. Carroll has also taken a minority share in the club which was taken over by Qatari group last week.
"From the first meeting with the manager, I just knew it was the right club," Carroll told The Athletic. "I had probably six or seven clubs on the phone at higher levels, driving distance from home, and more money, but for me, it was the whole package of the club.
"I could speak to the owners, and they'd tell me what the future was going to look like. I could also speak to the manager, and he could tell me what it would be like. I just felt like I wanted to be part of it."
On his own plans for the club, he said: "I think the main thing that I would like to see is the academy set back up.
"If you've got 60,000 kids in the area under 16, you've got an opportunity. With West Ham around the corner, The Academy of Football, look at the players they've produced over the years. To get that up and running is key for the club - it's a necessity, really.
"You look at the club and you think it's got potential. It's 30 minutes into London on the train. It's a fantastic area. I could go to a League One (third division) or a Championship (second) team, and be mid-table and play bits and pieces, not really enjoying it, and float around.
"Or I could come here, start from the bottom, and have a project where I can work on the pitch and off the pitch to hopefully bring something fantastic to the club in the area."