Aneke spent most of last season with Crewe and he returned for a second stint with the League One side back in August.
The midfielder has made 16 appearances so far this term and has been given permission to play in Crewe's FA Cup first-round tie at Wycombe on Saturday.
"We are delighted that Arsenal has granted us permission to play Chuks in the FA Cup against Wycombe," Crewe boss Steve Davis told the club's official website.
"He is an Arsenal player and they have always been extremely helpful to us. The letter and loan extension has come through so that is great news for us going forward.
"They have granted him permission and we are delighted to have him for an extended period as well. There is more to come from Chuks, I am certain of that. We haven't seen the best of him yet but he always works hard to learn and improve as a player.
"He has shown signs of that improvement in recent week and adds that extra bit of creativity to our play. He fits in nicely to the way we like to play."