The 18-year-old was the Baggies academy player of the year last season but rejected the offer of a lucrative pro deal in order to make the switch across the West Midlands.
“Tim is an athletic midfielder who is technically very good,” said Villa academy boss Mark Harrison.
“He has the ability to play as a holding midfielder or a box-to-box midfielder, who can contribute in both penalty areas.
“Tim has a lot of potential and we look forward to seeing him develop over the next few years.”
Iroegbunam, an unused substitute in Albion’s final Premier League match of last season, had been at The Hawthorns since the age of eight.
He posted a farewell message on social media which read: “I would like to say thank you to everyone at West Bromwich Albion who’ve helped me on my development as a footballer.
“You have all given me good times and memories I will cherish forever. Now my time has come to an end and I am looking forward to the next chapter. I wish the best to all my team mates and the coaches I’ve been with. It’s been an amazing 10 years.”