According to Major League Baseball, the Red Sox are the oldest team in baseball.
This is the release:
"The average age of 861 Major League players on 25-man active rosters, disabled
lists, and restricted lists as of April 1 was recorded at 29.46 years old. The Boston Red Sox are the oldest club in the majors with an average age of 31.33, while the Houston Astros
pace the National League at 31.09 years old. The Florida Marlins are the youngest team in baseball with an average age of 27.78, and the Oakland Athletics field the youngest squad in the American League at 28.20 years old.
In the American League, Detroit Tigers pitcher Kenny Rogers, 43, is the oldest active player, while New York Yankees pitcher Phil Hughes is the youngest at 21. In the National League, 45-year-old Philadelphia Phillies pitcher Jamie Moyer is the oldest, and Arizona Diamondbacks outfielder Justin Upton, 20, is the youngest."