The deal is pending a medical review.
It wasn't immediately known who New York was sending to Texas to complete the deal.
Gallo was a late scratch from the Rangers' lineup ahead of Wednesday night's game against the Diamondbacks, with speculation that a trade was in the works.
That proved to be the case, with the Yankees swooping in and acquiring arguably the fiercest bat on the trade market to go with fellow sluggers Giancarlo Stanton and Aaron Judge.
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Gallo has spent all seven of his major league seasons in Texas, but the Rangers -- an AL West-worst 36-65 entering Wednesday -- have been in sell mode, with Gallo their prized piece.
A two-time All-Star, the 27-year-old slugger ranks sixth in the AL this season with 25 home runs, to go with 55 RBIs and a .223 average. He had struggled mightily at the plate since the All-Star break, with zero home runs and a .067 average in the 10 games following, before breaking out Tuesday with a three-run shot against the Diamondbacks.
Gallo is among just eight rostered major leaguers with multiple career 40-HR seasons (2017, '18).
But he's also excelled in the outfield, winning a Gold Glove in right in 2020. He's tied for second in the majors with 12 defensive runs saved this season (tied for most among outfielders) and joins Toronto's Marcus Semien as the only players with 20 home runs and 10 defensive runs saved.
Gallo is also under team control through 2022.
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