The 29-year old wingback, who can also operate on the left side of midfield, has penned a deal with the Red Bulls and will be added to their roster pending receipt of his P-1 Visa and International Transfer Certificate and passing a team physical.
"David is an experienced international player, who can play on the left side both as a defender and a midfielder, and he provides us much needed cover," said Roxburgh.
"He is versatile and athletic and has competed at a high level. We are pleased to bring David to New York and look forward to his contribution as a member of the Red Bulls."
46-times capped Australian international Carney had been without a club since leaving Uzbekistani outfit Bunyodkor in September last year.