The 34-year-old former Southampton, Everton, Stoke and England striker joined the Reds in November and has scored four goals in 10 appearances.
Beattie's deal at the Crown Ground was due to expire on Wednesday but he will now continue to work alongside former Blackburn youth team-mate and Stanley manager Leam Richardson.
"It's fantastic to have a player like James Beattie with the quality he has on the pitch and the influence he has off it at our place," said Richardson in a club statement.
"It can only be a good thing that he's staying and hopefully it can help push us forward.
"I think people have seen the quality that he's still got in front of goal and the work ethic and appetite he's still got for the game.
"He's a great influence in the dressing room and with the younger lads he's second to none.
"He's had a large amount of offers to play in League Two and League One and even abroad, but in his words he wants to come and help and be part of something exciting.
"That's fantastic to hear and see in football these days."