The signing of the former Chelsea winger has faced backlash from Arsenal fans and criticism directed at Arteta.
In fact, Smith's former Gunners teammate, Paul Merson, stated that the deal left him "astonished."
However, in response, Smith told Tribal Football: "I haven't heard Merson's reasons for that. It came as a bit of a surprise in some ways.
"I believed his performance was steady, and he's at an age where he should only improve under Arteta, who is an excellent coach, make no mistake. He has the ability to enhance players, and he typically does.
"He can operate on both wings, which provides a great option to give (Bukayo) Saka some rest and to offer an alternative to (Gabriel) Martinelli, who has been a bit inconsistent.
"So, I don't agree with this. You know what? One could debate the price tag (£52m), but honestly, anyone who's reasonably good costs a fortune, right? Hopefully, it will turn out to be a good signing."
True Arsenal fans will support Madueke
When asked about the upset response from a segment of the Arsenal fanbase, Smith admitted it confused him.
He continued: "I don't understand it. I really don't. You have to trust your club and the professionals. These individuals are deeply analyzing the statistics, the underlying data, and everything else. They aren't just randomly selecting someone.
"These are professionals; they all have their roles. There's always a degree of risk with any signing. But given Madueke's experience in the Premier League, once he wears the shirt, the true Arsenal fans will rally behind him.
"With social media, there's always something that can arise, so hopefully, he can prove them wrong."
Alan Smith was speaking toTribalfootball on behalf of William Hill