The 37-year-old slugger, who homered twice in New York's 7-1 win over the Blue Jays on Tuesday, joined Tino Martinez (2005) as the only Yankees to hit 10 homers in a calendar month at age 37 or older.
"It's great to me," Soriano said. "When I left here [in 2004], I wasn't sad, because it's part of the game, but I thought that I had something to prove to myself, my teammates and the fans.
"I'm just playing my game. That's what I like to do. Focus every day, try to get better and try to show the people that I can keep doing it."
The Yankees were attracted to Soriano because of the power he would bring to the lineup, but he has proven to be helpful in other areas as well. Soriano's baserunning has been better than advertised, and manager Joe Girardi has also appreciated his outfield defense.
"He's played really, really good out there," Girardi said. "From what we heard, he said he worked really hard in Chicago at it."
Girardi believes that Soriano has responded to being dropped into a veteran clubhouse fighting for a playoff spot, comparing it to the effect that joining the Yankees seemed to have on Ichiro Suzuki after his July acquisition from the Mariners last year.
"It's kind of like Ich; Ich came from a club where it was mostly kids," Girardi said. "The Cubs are a lot of kids, so it may be a little more difficult to relate, in a sense. Now, he gets around people his age and it's probably easier."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.