Following a successful loan period at Stanley from the Cod Army last term, the 26-year-old centre-back is happy to sign a permanent deal at the club.
"It's good to be back," the defender said.
"I spoke to the gaffer (James Beattie) over the summer and listened to what he had to say about the club and I really wanted to be a part of that - hopefully we can have a good season."
Boss Beattie was also optimistic about Atkinson's potential impact at the League Two club during the season ahead.
"It's a great acquisition from the club's perspective," said the 35-year-old.
"Rob's a great player who we want to come in and play well for the club but I've said to him that we know he can play at a higher standard.
"Hopefully that will be with us and I think that it will."