"Tim will move to the Red Bulls for a nominal fee, subject to agreeing personal terms and passing a medical. He will travel to the U.S. in the next few days," Everton said on their website (www.evertonfc.com ).
British media reported the transfer fee would be about one million pounds ($1.55 million).
The 32-year-old attacking midfielder scored 68 goals in 278 games for Everton after joining the club from Millwall in 2004.
He has also scored 24 goals in 55 games for Australia and played at the last two World Cups in Germany and South Africa.