"It's a good day for me today to have the chance to put the uniform back on again," Soriano said after he went 0-for-5 with an RBI and a run scored in the Yankees' 10-6 loss to the Rays Friday night.
"This is a great organization, I played for (five years), to come back is an exciting moment for me."
Soriano batted cleanup and played left field for the Yankees in the first game of a three-game set against Tampa Bay at Yankee Stadium.
"We've obviously been trying to improve our offense this season, to no avail," Yankees general manager Brian Cashman said. "By far, he was the best available bat to date."
Of the estimated $24.5 million Soriano is owed through the end of next season, the Cubs are going to pick up about $17.7 million and the Yankees will cover the remaining $6.8 million, sources told ESPN. Soriano is scheduled to make $18 million next season, $5 million of which will be paid by the Yankees, the sources said.
Major League Baseball had to approve the dollar exchange for the trade to go through. The Cubs will get Class A pitcher Corey Black from the Yankees.
Soriano is excited to join a team in a playoff race. The Yankees are 3½ games out of a wild-card spot.
"I'm happy that I have the opportunity to come back to New York, where I started my career," Soriano said. "I'm happy I can try to help the team to win and make the playoffs."
Yankees manager Joe Girardi said he will use Soriano in left field and as the designated hitter, and the outfielder will provide much-needed power from the right side. The Yankees last received a homer from a righty on June 25, courtesy of Jayson Nix.
"I hope it makes us better, a lot better," Girardi said. "You're able to split up your lefties a little bit, too, by putting him in the middle. Hopefully it helps our lineup."
Soriano, 37, began his career with the Yankees -- playing for them from 1999-2003 -- and was all smiles as he met with former and new teammates before the game. Soriano played with Derek Jeter, Mariano Rivera and Andy Pettitte during his previous stint with the team.
"It was great when I used to be with the Yankees," Soriano said Wednesday. "My best friend with the team is Jeter, and he's still there. Mariano is still there too. And me and [Robinson] Cano are good friends, too, because we're from the same town. I could feel very good with the Yankees because I've been part of the family before with them."
Soriano is batting .254 with 17 home runs and 51 RBIs this season and has heated up in July, with eight homers and 16 RBIs. He's 11 hits shy of 2,000 for his career and 11 home runs short of 400.
"He's played there before," injured Yankees outfielder Curtis Granderson said earlier in the day at the team's spring training complex in Tampa, Fla. "That's one thing that is a difficult thing to adjust to.
"You've got to come to New York and can you handle it, can you not? Obviously he had in the past."
Girardi added: "It's something he's very familiar with, and there are still people here he played with and he'll be comfortable. I think it's important. Sometimes it takes players some time to adjust coming in here, but it shouldn't be any issue with him."
Soriano will wear No. 12, which he wore in his final two seasons in New York. Vernon Wells, who had worn 12 this year, will be No. 22.
Mark Teixeira, who played with Soriano in Texas in 2004-05, likes the move.
"He's a great addition, one of my favorite teammates of all time," Teixeira said. "We had a great time together. He's happy. He's like Robinson Cano, one of those guys that's always happy. Loves playing the game. Incredible talent. I love the move."
Soriano never has played a regular-season game at the new Yankee Stadium. He did, however, hit a home run in his lone game at the ballpark -- in April 2009, when the Cubs played a pair of exhibition games at Yankee Stadium before the official opener.
"This is my house. I play here. I start my career [here]," Soriano said. "I think I have a great moment here with the Yankees and I'm happy when I play here, so that's why I come back here."
The Yankees also announced that outfielder Thomas Neal was optioned to Triple-A Scranton/Wilkes-Barre.
Information from The Associated Press was used in this report.