The tradition starts now. An award that will be annually presented to each league's best relief pitcher has been named after two recently retired greats, Major League Baseball announced Wednesday.

The American League's top reliever will be given an award named for Mariano Rivera, and the National League winner will receive a trophy named for Trevor Hoffman. Rivera and Hoffman, Nos. 1 and 2 in career saves, spent their entire careers pitching in their respective leagues.

Rivera, a 13-time All-Star, earned all of his 652 saves for the Yankees. Hoffman, who spent most of his career with the Padres but also pitched for the Marlins and Brewers, racked up 601 career saves.

The new honors, beginning this season, will replace MLB's Delivery Man of the Year Award, which was given to one reliever each year, as opposed to one reliever per league.

"Both Mariano and Trevor represented our sport magnificently on and off the mound and earned the universal respect of our fans in their legendary careers," Commissioner Bud Selig said. "I believe it is appropriate to redefine an existing award in honor of their contributions to baseball, and I am delighted that many of the most decorated relievers in history will select the winners."

The award winners will be determined by a vote of other great relievers. Rivera and Hoffman will be joined by Dennis Eckersley, Rollie Fingers, Goose Gossage and Bruce Sutter, who are the four living relievers in the Hall of Fame, and Lee Smith, John Franco and Billy Wagner, all of whom are among the top five in career saves.

The nine voters will rank the top three pitchers in each league based solely on regular-season performance, and each of their ballots will use a 5-3-1 weighted point system.

Hoffman, who retired after the 2010 campaign, won the Rolaids Relief Man Award (which was solely based on statistical achievements) twice. Rivera, a five-time World Series champion with the Yankees, won the Rolaids Relief Man Award five times and the MLB Delivery Man of the Year Award three times.