The London-born midfielder became Steven Gerrard's seventh summer recruit.
The Ibrox club fought off plenty of competition to land the 22-year-old with a rafts of clubs interested, including Celtic, Brentford and Bundesliga sides.
Allen, who is with the team in their Portugal training camp, reckons the signing of Aribo is a real statement.
He told the Daily Record: "We’ve fought off a lot of competition for Joe. I don’t think it’s any secret that teams were interested.
“But he felt that this was the right project for him.
“We’re really satisfied with it and he was one of our targets from very early doors.
“In terms of Rangers’ pulling power, the proof is in the pudding when a player like that signs on the dotted line.
“We’re under no illusions about the level of this club. With the exposure, 50,000 fans every other week, this club is massive.
“When you look under the skin and see what it’s all about, it becomes a much easier decision for players to make."
With Gerrard keen on another centre-back, Allen has refused to rule out further signings.
“I’m pleased to say that it’s gone well so far.
“How many more do we want? I’ve always said we’ll never say that we’re done until the window is closed.
“We’re satisfied with what we’ve done to date – let’s just see what else happens.”