Custom-built for Anthony in 1975, the 3,881-square-foot house contains a den, an office, a gym, two fireplaces, two bedrooms and three bathrooms.
"We built it to take advantage of the tremendous views," he said of his hillside home, which sits on about a quarter-acre on a cul-de-sac.
Anthony, who turned 90 this year, used the house for years to run a business selling big-band CDs. He plans to play at a belated celebration marking his birthday this month.
He has performed with Frank Sinatra, Glenn Miller and Jimmy Dorsey, among others. Anthony and his band appeared in several movies and on the late-'50s variety show bearing his name.
Anthony said he is selling to move closer to a friend in Beverly Hills.
James Campbell and Luis Pezzini of Sunset Strip Realty are the listing agents.