The Cardinals said Matheny, 41, will be officially introduced Monday.
Matheny retired as a player in 2007 after catching for the Cardinals from 2000-04. He has served as a roving coach in the St. Louis organization since then but has no major-league experience as a full-time coach or manager.
La Russa walked away from the job after guiding the Cards to the 11th World Series victory in franchise history -- becoming the first manager in baseball history to quit after winning a world championship.
Also officially interviewed for the job were third-base coach Jose Oquendo, Class AAA Memphis manager Chris Maloney, Chicago White Sox third base coach Joe McEwing, former Chicago Cubs second baseman Ryne Sandberg and former Boston Red Sox manager Terry Francona.