And that's in addition to former Yankees killers and Boston stalwarts Nomar Garciaparra and Derek Lowe, who also play big roles for Torre's current team.
"Who would have thought that a few years ago, right?" Garciaparra asked. "That's the way baseball has gone. You never know who you're going to play with, who you're going to play for; you just go out and play."
Torre knows firsthand the type of player Ramirez is after his Yankees played Ramirez's Red Sox 18 or 19 times a season, not to mention their many playoff battles over the years.
That's why he immediately got excited when Dodgers general manager Ned Colletti told him a Ramirez deal was possible Thursday morning.
Although Ramirez recently clashed with Boston's front office and has a reputation of marching to the beat of his own drum, Torre feels confident in bringing in Ramirez because his teammates have never had any issues with him.
"If you feel somebody's going to help your club, you've got to find a way to make it work, and that's my job, to find a way to make it work," Torre said. "If it's a challenge, it's a challenge. I look forward to it."
That's a challenge Torre often encountered in New York, when the Yankees brought in high-priced player after high-priced player.
However, when making a move for a personality such as Ramirez in New York, Torre knew he had a strong core group of veterans in contrast to the impressionable youngsters in Torre's current clubhouse.
"My biggest concern is the impact on the rest of the team," Torre said. "This is the thing that concerns me the most -- not that I'm worried about it. I'm saying that's the thing I'm more aware of."
As for how it affects the rest of the players on the field, Torre has already been dealing with a juggling act of having four outfielders for three spots since Juan Pierre returned Friday.
After adding an everyday player like Ramirez, Torre said he's not sure whose playing time that would take away from, but he feels like the odd men out will understand the reasoning because of the impact a 12-time All-Star like Ramirez can bring the Dodgers.
Whoever does become a bench player, however, will add punch to Los Angeles' bench.
"I think it has a trickle-down effect," Torre said. "We're one player stronger, and that one player is unfortunately going to take playing time away from an outfielder, but again, the impact on the 25-man [roster] is obviously important, and that was the biggest plus."
Torre called Ramirez "one of the best handful of hitters in this game" and said it's "crazy" how trades now are being made for reasons other than pure talent since the start of free agency.
Torre recalled the type of streak Ramirez can roll off when he gets in a groove, remembering especially a time when he walked David Ortiz to get to Ramirez, only to see the slugger knock one off the left-field wall. He expects the protection Ramirez will provide to the rest of the Dodgers to make an immense difference.
"Now [that] Manny's in the middle, it's going to make everybody above him find better pitches to hit," Torre said.
The trade has one final byproduct that Torre's very used to from his days under George Steinbrenner in New York.
"Now there's more pressure," Torre said. "I'm supposed to win."