The youngster joins on a three-year contract and for an undisclosed fee.
Iroegbunam told evertontv: "I’m very pleased. Everton is an amazing club, a big club and I’m just really happy to join and I can’t wait to get started.
"It was a move that I didn’t want to pass by. I wanted to take the opportunity.
"When I spoke to Kevin (Thelwell, Everton football director), he told me more about the Club – its history, the future and where they see me playing. It made me feel very excited because there are big things coming, especially with the new stadium.
"When I’ve been to Goodison as an opposition player, I’ve seen how the Everton fans are. You can tell straight away what the atmosphere is like – they are always backing the team. I’m going to work hard for them.
"I just can’t wait to get started. I’m going to give everything and I can’t wait to show what I can bring to this club."
He also said: "I’d say I’m a player who does a bit of both – I like to get forward, carry the ball up the pitch but, at the same time, I like to get stuck in, win tackles and work hard.
"It was very important for me to get the move sorted quickly. It means I can get settled in and come in from day one and take my chance to impress from the start of pre-season.
"I know the manager likes his teams to be on the front foot, be direct and work hard. For that you need to be fit and being here for the full pre-season is going to help me get up to those fitness levels to do all of those things. I’m ready for it."
Everton manager Sean Dyche said: "We're pleased to add Tim to our midfield options. He is a young player who is still learning and developing but clearly has a lot of the qualities we want in that area of the pitch.
"My coaching staff and I are looking forward to starting to work with him in pre-season."
Director of Football, Kevin Thelwell, added: "We are delighted to have been able to move quickly to bring Tim to Everton. He is a player we have been following closely and we believe he has the skills and characteristics to be a strong addition to our midfield.
"At 20 years old, he is a young and hungry player who has already gained some impressive experience and we look forward to helping him to continue to develop and fulfil his obvious potential."