The 66-year-old, who served as CEO at Goodison Park between 2004 and 2009 and now runs a football consultancy advising elite clubs, also singled out Denmark international Thomas Gravesen as another of his favourite imports.
Arteta joined Everton in January 2005 from Real Sociedad on an initial loan before signing permanently in the summer.
He was seen as a replacement for Gravesen, who had recently signed for Real Madrid, and went on to help the Toffees secure European qualification.
Arteta was one of the best player in the world
Arteta made 209 appearances for the Merseysiders, notching 35 goals and 36 assists.
The Spaniard, who also played for Paris Saint-Germain and Rangers, eventually left for Arsenal in 2011 for a reported fee of £10million before retiring in 2016.
When asked to choose his favourite signing of his time at Goodison by Football Insider‘s Inside Track podcast, Wyness said: “Mikel Arteta. I was very proud of that one.
“We had a good negotiation with his agent. It was tough, but we got him.
“He was great.
“But my favourite player from my time at the club was Thomas Gravesen. I ended up selling him to Real Madrid.
“Tommy was a great character.
“We had a great squad and the club really came together and was united.
“Everything worked, and that’s what happens when you really work as a group with strong leadership.”
“Richard Masters has unleashed what I consider to be a legal merry-go-round.
“There’s the legal action from relegated clubs, there’s talk of Everton suing Man City or Chelsea. If I’m a chief executive, I’m looking at spending 30% of my budget on KCs rather than a left-back.
“That has put the Premier League into a cycle of big issues. I think Masters has to be looked at in terms of how he’s led the league into this situation.