The vote was conducted via conference call on Wednesday.
Sherman and Jeter -- the former New York Yankees shortstop will be the CEO -- officially will take over upon the close of the $1.2 billion deal, which is expected to happen Monday, the Orlando Sentinel reported, citing a source familiar with the process.
"I wish the best to (owner) Jeffrey Loria and (outgoing team president) David Samson," commissioner Rob Manfred said in a statement. "During their tenures, the Marlins won the 2003 World Series, hosted this season's successful All-Star Week at spectacular Marlins Park and eagerly supported our efforts to grow the game internationally.
"I congratulate Mr. Sherman on receiving approval from the major league clubs as the new control person of the Marlins and look forward to Mr. Jeter's ownership and CEO role following his extraordinary career as a player."
The $1.2 billion price tag of the sale is the second-highest in a history for a MLB team, behind only the Los Angeles Dodgers' $2 billion sale in 2012.
Loria purchased the team for $158.5 million in February 2002, and a year later, the then-Florida Marlins won their second World Series. The Marlins haven't been back in the playoffs since, and they haven't finished above .500 since 2009.
The Marlins had a team-record $115 million payroll on Opening Day this year.
"Owning the Miami Marlins has been one of the singular honors of my life," Loria said in a statement. "I want to thank our players, coaches and employees for the incredible dedication they brought to this pursuit. I also extend my heartfelt thanks to our loyal fans for your passion and commitment to what we built together.
"Owning a sports team, like most things in life, is temporary. An owner is merely the steward of a franchise, shepherding the advancement of this public trust during his or her tenure. I'm very proud of our collective achievements during the past 15 years, including bringing a World Series, new ballpark, World Baseball Classics, and an All-Star Game to our community.
"But part of the deal is acknowledging when it's time to pass the baton to the next generation, and wish them well in taking things to the next level. With that in mind, I can't think of anyone better suited than Bruce Sherman and Derek Jeter. They are true baseball people, as well as true gentlemen. I have every confidence in their ability as the next stewards of the Miami Marlins to take us to new heights.
"Although my ownership is in the past, my love of baseball is not. As an avid fan, I'll be eagerly watching from the sidelines."