Rogers, 23, who has impressed during the tournament in North America, will fetch a transfer fee of £117 milllion and will sign a seven-year deal with US-owned Chelsea, the reports said.
His departure from Villa follows that of Belgium World Cup midfielder Youri Tielemans, who joined Manchester United this week.
Villa have moved to sign reinforcements and announced on Friday 20-year-old Switzerland World Cup winger Johan Manzambi is joining from German side Freiburg for a reported club record fee of just over £50m.