The Whitney is the most prestigious summer race for older dirt horses in the US and carries a purse of $1 million.
Owned by Godolphin and trained in the UK by Saeed bin Suroor, last raced on June 8 when third behind Mitole and McKinzie in the G1 Metropolitan Handicap at Belmont, his first start since a second hard-fought victory in the Dubai World Cup in March.
"He is doing great," Bin Suroor said. "He had a very nice work, his last piece of work over the gallops at Newmarket this week and I'm happy with him.
"He's in good form and improved from his last race at Belmont. He's sound, happy and healthy and that is what you want."
Thunder Snow has won or placed in 12 G1 races from 1400m (seven furlongs) to 2000m (1¼ miles) in five countries—France, Ireland, UAE, UK and USA.
He is yet to win in America in three races for a second and two thirds.
Last year he was second in the G1 Jockey Club Gold Cup before a third in the Breeders' Cup Classic.
"He will be ready for the Whitney and the nine furlongs will suit him better than the mile," Bin Suroor said.
"He will be more settled in the Whitney, but he will also have to be handy in the race."
Thunder Snow has earned $US16,511,476—the highest of any active thoroughbred and currently third on the all-time prize money list, just over $900,000 behind fellow Dubai World Cup winner Arrogate and less than $US2 million astern of Australian wonder mare Winx.
Bin Suroor confirmed that the son of Helmet shipped to New York on Wednesday.
The $US6 million Breeders' Cup Classic at California's Santa Anita Park on November 2 is the ultimate goal for Thunder Snow this year.
He will try to make history as the first horse ever to win the Dubai World Cup and BC Classic in the same year.
He could return to Saratoga for the G1 Woodward on August 31 and go to Belmont for the Jockey Club Gold Cup on September 28.