The announcement comes after Peters was named more than a year ago to head the Value Trust fund, which Miller has managed for 30 years.
"We have had a long and thoughtful transition process going back more than six years," Miller said in a statement. "We recognized Sam as a potential portfolio manager for Value Trust when we hired him in 2005, then observed his steady hand during the 2008 financial crisis, and last year named him co-manager of Value Trust for the purpose of succeeding me as sole manager."
Since its inception in 1982, the Value Trust fund has become synonymous with Miller, who has the unmatched record of beating the benchmark Standard & Poor's 500 index for 15 consecutive years. His streak was broken in 2006.
In recent years, the Value Trust fund has struggled. It lost 55 percent in 2008, becoming one of the worst performers among its peers. But the fund has been bounced back some.
While handing over the reins of the Value Trust, Miller will continue to manage the Legg Mason Capital Management Opportunity Trust.
Besides the Value Trust, Peters will continue to co-manage the Legg Mason Capital Management Special Investment Trust and mid-cap strategy with Albert Grosman.