The announcement comes after Peters was named more than a year ago as successor to Miller, who has managed the Value Trust fund for almost three decades.
In an interview, Miller, 61, described the move as a long-planned transition to give Value Trust its next generation of management. He said he timed the change to coincide with the 30th anniversary of the fund's launch.
When asked if this marked a gradual transition toward retirement, Miller said, "I haven't really thought about that."
He added that by managing fewer funds, he hopes to have "less bandwidth taken up."
"Normally for most people, one fund is enough," Miller said.
Miller praised Peters' "steady hand" during the 2008 financial crisis, adding that Legg had eyed Peters as a potential portfolio manager for Value Trust from the day he was hired in 2005.
Since its founding 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, Value Trust has struggled, losing 55 percent in 2008 and becoming one of the worst performers among its peers. Miller beat the S&P 500 again in 2009 but has lagged behind it since then. Investors have headed for the exits, helping to reduce the fund's assets from more than $20 billion a few years ago to less than $3 billion now.
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. Peters dismissed speculation that he would be less bold than Miller in betting on undervalued stocks and sticking with them for an extended period.
"On some vectors at this point I'm probably more aggressive than Bill is," he said in an interview. "The key for me is, when the opportunities are there from a valuation standpoint, they'll be more than fully reflected in the fund."