The Premier League club said Monday on its website that Cahill ''will move to the Red Bulls for a nominal fee, subject to agreeing personal terms and passing a medical.''
The 32-year-old midfielder had been linked with a move away from Merseyside this summer, with clubs in the Middle East and China thought to be interested.
But the States appeared to be the Australia international's preferred destination, with the Red Bulls believed to capture the midfielder's signature.
Cahill is expected to travel to the United States in the next few days.
The Australian midfielder joined Everton from Millwall in 2004, scoring 68 goals in 278 appearances.
Recently, the Red Bulls acquired Sebastien Le Toux from the Vancouver Whitecaps via a trade, giving New York three forwards with Henry, Le Toux and Kenny Cooper in attack.
Information from The Associated Press was used in this report.