Arsenal are in the process of finalising the transfer for Rekik from Hertha Berlin.
Rekik, 19, has been training with the club ahead of the move and is an U21 international for Tunisia.
He will initially join up with the club's U23 squad and it is understood a loan move has not been ruled out.
"We will announce it when we can, he's a young talent and we have been following him for a while," Arterta told reporters on Thursday.
"We believe he has a very bright future, but we will give more details soon."