Bloom and Neander were previously the team's directors of baseball operations and Friedman's top assistants.
The pair replaces departed VP Andrew Friedman, who left to become the general manager of the Los Angeles Dodgers earlier this week.
Friedman had been an investment banker before joining the Rays organization. Ten Rays players acquired by Friedman made their first All Star team while playing for Tampa Bay. He had been the Rays' VP of baseball operations since 2005, when he was 28 years old. Under his leadership, the Rays qualified for the playoffs four times, after missing the postseason in their first 10 seasons.
Tampa Bay advanced to the World Series in 2008 but lost to the Philadelphia Phillies in five games. The Rays had the second-lowest payroll in the majors that season, and won a total of 97 games. Friedman was named Executive of the Year by the Sporting News that year, the youngest winner in the award's 72-year history.
Tampa Bay finished 77-85 this season and missed the playoffs.
- Dan Gartland & Paul Palladino