English is expected to sign a five-year deal for about $350,000 per year, a person briefed on the deal told ESPN's Joe Schad on Saturday night.
A news conference was set for Monday.
English, 40, just finished his first season guiding the Cardinals' defense. Before that, he was the defensive coordinator at Michigan under Lloyd Carr. Louisville's defense showed great improvement this season early on before giving up 98 points in its final two games after injuries thinned the unit.
English would become just the fifth African-American head coach among the 119 Football Bowl Subdivision schools.
Eastern Michigan went 3-9 this season, leading to the firing of Jeff Genyk, who was 16-42 in five seasons in Ypsilanti.
Louisville officials knew English wanted to become a head coach when it signed him to a two-year contract in January. The Cardinals are likely to promote linebackers coach Bill Miller to defensive coordinator to replace English. Miller has been a defensive coordinator at Arizona State, Michigan State, Oklahoma State and Miami.
Brian Bennett is a college football reporter for ESPN.com. ESPN college football reporter Joe Schad contributed to this report.