"I've never been in this situation," Overbay said. "It's kind of been a whirlwind. I've been around this game, and things can change real quick."
Rivera hit .305 (18-for-59) with five doubles and five RBIs this spring. Instead, the 34-year-old was cut after the Yanks signed Francisco on March 11 and added Overbay on Tuesday.
General manager Brian Cashman said Rivera had a contractual deadline to be added to the club's 40-man roster on Thursday. Rivera said he thought he had done enough to make the club.
"This is the New York Yankees," Rivera said. "You never know."
Cashman said that the team has not made any final decisions on its roster. Overbay's Minor League contract could have expired on Friday, but he will instead go north with the club for the exhibition games against the Nationals in Washington, D.C., on Friday and the Army Black Knights at West Point on Saturday.
"I'm just along for the ride and see what I can do," Overbay said. "It's hard to know what to expect. I just try to be as professional as I can and try to have good at-bats, and show them what you've got in a short amount of time."
With Rivera deleted from the Yankees' roster, it is probable that Kevin Youkilis will play first base on Opening Day against the Red Sox, since left-hander Jon Lester is scheduled to start for Boston. Jayson Nix is the likely choice to play third base in the season-opening lineup.
Overbay hit .259 with a pair of homers in 65 games last year with the D-backs and Braves. He signed with the division-rival Red Sox in January before his release earlier this week.
Francisco hit .240 with four homers in 82 combined games last season with the Blue Jays, Astros and Rays. He signed with the Indians this offseason, but requested his release from Cleveland in March and signed with New York later that same day.
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.