The deal is pending a medical review and is expected to be made official Thursday.
The Rangers will receive right-hander Glenn Otto, second baseman Ezequiel Duran, shortstop Josh Smith and second baseman/outfielder Trevor Hauver from New York, sources told Passan. Texas will send an additional player, pitcher Joely Rodríguez, to New York to complete the blockbuster.
Gallo was a late scratch from the Rangers' lineup ahead of Wednesday night's game against the visiting Arizona Diamondbacks, with speculation that a trade was in the works.
New York's left-handed hitters have struggled this season, ranking last in the majors in average (.197), 28th in home runs (22) and OPS (.633) and 29th in hard-hit rate (33%).
Gallo should help.
He has spent all seven of his major league seasons with Texas, but the Rangers -- an American League West-worst 36-65 entering Wednesday -- have been in unloading mode, with Gallo their prized player.
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-homer seasons (2017, 2018).
He also has excelled in the outfield, winning a Gold Glove in 2020. He leads the majors with 14 defensive runs saved this season and joins the Toronto Blue Jays' Marcus Semien as the only players with 20 home runs and 10 defensive runs saved.
Gallo is owed $2.2 million from his $6.2 million salary. He is eligible for arbitration next winter and can become a free agent after the 2022 season.
Gallo gave what became a prophetic goodbye to Rangers fans when he started thanking them in a postgame interview Tuesday night on the team's television broadcast. He told reporters after that he didn't want to miss an opportunity to thank everyone.
"We don't know the future, and I don't want to like miss an opportunity to tell everybody I appreciate it,'' Gallo said. "I've been 10 years here. I remember last year when I almost got traded, there was like a lot that I was thinking, 'Man, I wish I would have done this, I wish I would have said something.'
"I want the fans to know that I appreciate everything they've done for me and supporting me and buying my jerseys and whatnot. You know, I really appreciate it.''
The Rangers got a strong package in return for Gallo.
Otto, a fifth-round pick of the Yanks in 2017, has split time between Double-A and Triple-A this season, going 7-3 with a 3.33 ERA in 12 starts. He has posted sub-4.00 ERA in all four of his minor league seasons.
Duran, a 22-year-old from the Dominican Republic, had been off to a hot start in Class A this season, with 12 home runs, 48 RBIs and a .290 average in 67 games for Hudson Valley.
Smith, also with Hudson Valley, was the Yankees' second-round pick in 2019. He has 17 steals and 44 runs in 39 games this season, while hitting .324.
And Hauver, a third-round pick last year, was hitting .288 with nine home runs and 49 RBIs this season, his first in the minors.
The last-place Rangers are on pace for their first 100-loss season since 1973, the franchise's second season in Texas. Their last winning season was 2016, when they won the AL West, before getting swept by Toronto in a best-of-five division series.
Information from The Associated Press was used in this report.