When Hinch was hired as manager of the Arizona Diamondbacks in 2009, he was just 35- the same age as former Yankees and current Orioles manager Buck Showalter. When the Cleveland Indians hired former MLB C Eric Wedge as manager prior to the 2003 season, he was just 34 year old- the youngest manager in MLB history who was not a player- manager.
The manager of the last World Series Championship team in Washington was just 27 when he took his first job behind the bench. It was 1924 and the team named starting 2B Bucky Harris as their manager. The 27 year old led the team to a World Series Championship in his first season and the Senators made it back to the World Series the following season. Harris would lead the 1947 Yankees to the World Series among his 29 seasons behind the bench and he would be inducted into Baseball's Hall of Fame in 1975. Lou Boudreau was just 24 when he was put behind the bench to lead the Cleveland Indians in 1942. He was a player- manager through the 1950 season, which included the 1948 World Series Championship. Of course, that was the last time the Indians won the World Series, a place they have only returned to play in 1954, 1995 and 1997. Boudreau was inducted into the BBHOF in 1970.
I give the title of the youngest MLB manager in its history to Boudreau over that of the younger Roger Peckinpaugh. Though Peckinpaugh later managed the Indians from from 1928-1933 and again in 1941, he was the interim manager of the New York Yankees during the 1914 season. He was just 23 at the time and was named interim manager to succeed Frank Chance, who had submitted his resignation with 20 games to go in the season. Though Peckinpaugh was the starting SS and team captain, he was not retained for the 1915 season, as the job went to Bill Donovan. Peckinpaugh technically is the youngest recorded player (or non player) to run a team from the bench, but he was only holding the fort down until a new manager could take over the next season.
On a not completely related topic, outside of the Angels Mike Scioscia (2000), the longest tenured big league skippers right now are Giants Bruce Bochy (2007) and Padres Bud Black (2007), Yankees Joe Girardi (2008) and Royals Ned Yost (2010). Next, in terms of seniority, is a tie between Mets Terry Collins, Pirates Clint Hurdle, Dodgers Don Mattingly and Braves Fredi Gonzalez (all hired prior to the 2011 season). Athletics manager Bob Melvin took over the team during the 2011 season.