The former Everton boss was named as Sam Allardyce's replacement at the Stadium of Light last week after the latter quit his role to take the England job.
The Scottish manager has had a rough time of it lately after being sacked by Real Sociedad and Manchester United over the past two years or so.
But those struggles do not detract from the magnificent job that the 53-year-old did at Everton for over a decade.
Moyes was given a four-year deal, and Quinn, a former chairman and player at Sunderland, says that the length of his contract indicates a sense of stability that the North-East club - who have had five permanent managers in five years - have lacked in recent time.
"He can really take it on from where Sam had it," Quinn told Sky Sports.
"He signed a four-year deal which is really good news, that smacks of stability, which we haven't been able to say about Sunderland for quite some time.
"I believe what he possesses and his desire to get back as being renowned as a top manager - I think the mix is really good."
Sunderland fans will have grown accustomed to the pain of relegation battles and the joy of winning them, with Allardyce, Dick Advocaat and Gus Poyet all coming perilously close to being relegated in recent years.
But under Moyes, the supporters will be looking forward to the drip and drab of mid-table finishes initially, before hoping the Scot can help elevate them to a new plateau.