The 27-year-old got the shutout for the United States on Thursday night in a 1-0 win over El Salvador in a World Cup qualifier.
New England answered with a trialist offer that became a contract.
I need to get my legs back under me and even myself out because I was on crutches for a little while and in a walking boot.
Turner has enjoyed a similar rise at the international level, making 13 appearances for the U.
He is reportedly going to cost Arsenal just £5.
Aaron Ramsdale and Bernd Leno are the senior goalkeepers on the Gunners roster, with Ramsdale earning 19 of the 22 appearances so far in league play.