The England international joins the Reds for a mooted £12 million.
Ayre told liverpoolfc.com: "I think he fits all the profile of everything we've talked about in the past - a young player, a prolific talent and a prolific goalscorer in the position he plays in. We've always said we want to keep adding great talent to this team and squad.
"It's another great example of people showing their faith in the investment we're making and the project that Brendan is undergoing. Every transfer window, we continue to add, improve the squad, improve the group and support the manager. We've seen the football get better and the squad get better. That's got to continue and this is another step in that direction, but a very important one."