The former Celtic defender will sign a five-year contract with the Gunners in the coming days.
He has three years left on his existing contract but the club is keen to make him sign an improved contract in the summer.
He was one of the standout performers for Arsenal in a disappointing season where the club finished eighth in the Premier League.
The 24-year old defender made 27 appearances for the North London club last season and Arteta has backed Tierney to become Arsenal captain one day.
“I think he can be Arsenal captain as he has the respect and admiration of every member of the staff and every player,” said Arteta in January.
“It is just the way he is. He does it in a natural way.
“He is a really shy boy as well but he represents all of us in the club; all of the values that we want to instil and are in the DNA in this club.”
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