"It's extremely difficult, because he's been a great Yankee and a great player," manager Joe Girardi said.
Soriano was batting .221 over 67 games this season, and he hadn't been able to display the power he showed after the Yankees traded for him last June, hitting only six home runs. He totaled 17 homers and 50 RBIs over 58 games with New York in 2013.
When pitching depth became a concern, Soriano was the odd man out in an outfield that already included veterans Ichiro Suzuki and Carlos Beltran.
"He never made excuses," Girardi said. "Never. I knew his wishes. I knew he wanted to play every day in the outfield. But that was Ich. That was Carlos, too. It was kind of difficult."
The 38-year-old spent parts of seven seasons at the big league level with New York, and he was named to seven straight All-Star Games from 2002-08 with the Yankees, Rangers, Nationals and Cubs.
Teammate Derek Jeter was especially sorry to see Soriano go.
"Soriano's like family to me," Jeter said. "Played together with him for a long time. When he first came up, and then obviously, coming back now. So Sori's had a tremendous career here in New York. He's done a great job. It's difficult for him this year. Any time you talk about a player that's used to playing every day not playing every day, it's kind of hard to be productive.
"I feel for him. I'm going to miss him, but I will be in touch with him because he's like a brother for me, and he should be proud of what he's been able to do -- not only in the past but this year as well. I wish him nothing but the best."
Billings was 4-4 with a 5.31 ERA in 11 starts at Triple-A this year. He allowed four runs in four innings vs. the Angels on April 25 in his lone appearance for the Yankees this season.
The 28-year-old is expected to be available in a relief role for the short term, but Girardi said Billings will not be filling the rotation hole on Monday.
"We felt we needed more pitching today," Girardi said. "If something happened to Hiroki Kuroda early today, we'd be in a pickle, so we called up Billings. Our bullpen has been extremely taxed.
"For Sori, it's a guy who came in and did a tremendous job for us last year. He's had his struggles this year, and he's a guy who's used to playing every day. It wasn't everyday at-bats for him, so maybe it was harder for him to get going."