Arsenal have been finalising a £5.8million deal that would include an additional £2m in add-ons for the 27-year-old keeper.
However, Berhalter confirmed that the deal had been completed by admitting the American international would be leaving for Arsenal following USA's victory over El Salvador.
Berhalter said: "[Turner] Went to Fairfield University, was undrafted out of college, now he's playing with the national team and he's headed to Arsenal.
"It's just an amazing story and it's all down to him, his work ethic, his belief in himself and his never give up attitude.
"It's a great story and Matt is a great guy, a great teammate and we're lucky to have him.
"Tonight was an example of where he did everything that he had to do. He was calm in all situations.
"Wasn't tested much but was there when we needed him and he looked like a player that's going to Arsenal, for sure."
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