Chrisene, 16, goes straight into Villa's academy having made five senior appearances for the Grecians.
The England Under-16 international also played three EFL Trophy games and made one League Two appearance last season.
“Ben goes with our best wishes," Exeter manager Matt Taylor said. “He's gone to a Premier League club, which we're delighted about.
“However, it's a shame we're losing our players before we get the chance to really work with them."