Olson, a left-handed reliever, appeared in 11 games for the Mariners in 2015. He posted a 5.40 ERA in 13.1 innings pitched. He had a 2.08 ERA against left-handers in Triple-A, per MiLB.com, so he could become a lefty specialist for the Yankees in 2016.
Torreyes had a brief stay with the Dodgers last year, making eight plate appearances and going 2-for-6 at the plate. In the minors, he featured as a second baseman, third baseman, shortstop and even left fielder. He spent the majority of his time up the middle, though, so he'll likely play second or short predominantly next year.
Rosenthal noted Los Angeles had previously designated both players for assignment.
Segedin has yet to appear in a major league game, spending 2015 with the Yankees' Double-A and Triple-A affiliates. In 71 games, he hit .287/.360/.426 with seven home runs and 24 runs batted in. Should Yankees third baseman Chase Headley get injured, Segedin could fill in as a short-term replacement.
None of the three players moved will feature in his respective team's Opening Day plans without an outstanding showing in spring training.
However, they'll all provide depth over the course of the year in case the major league roster becomes depleted.