Neil was appointed as PNE boss on a 12-month rolling contract on Tuesday.
Bryson, who was North End captain when they won the Third Division title in 1996, has liked what he has seen of his fellow Scotsman.
On his CV, Neil can boast promotions both in England and Scotland.
He guided Norwich City to the Premier League in 2015 and the year before, Hamilton were promoted to the Scottish Premiership on his watch.
Bryson told the Post: “Neil seems a pretty level-headed individual.
“What he did at Norwich was good, getting them up to the Premier League.
“Before Neil went down to Norwich, he led Hamilton to promotion in Scotland.
“He looks like a very decent up-and-coming manager who maybe lost his way a little bit in the latter stages at Norwich.
“There is a lot of potential and I do think that he will suit Preston.
“We are not the biggest of clubs in the Championship and he will know that he has to work with a smaller budget than some of the other clubs.
“Traditionally, Scottish managers have tended to do well at Preston.
“So in my eyes, Neil is a wise appointment.
“He knows the division and will get to know quickly what Preston as a club are about.
“Yes, he will have had more money to spend at Norwich but I’m sure he’ll be able to get people in here.”
Neil follows a long line of Scots who have managed at Deepdale down the years.
David Moyes, Craig Brown, Billy Davies, Alan Irvine and Darren Ferguson are five Scots who have sat in the manager’s office since 1998.
And there were plenty more before.
Said Bryson: “I wouldn’t say that every Scotsman who has managed Preston have been successful but quite a few of them were.
“The club traditionally has had links with Scotland, I will always refer back to George Ross who had a great career as a player here.
“It is good to get this done quite early in pre-season, that allows the players to focus on training and get themselves in the right frame of mind to face a tough start to the season.
“There is the continuity of the backroom staff staying here.
“Steve Thompson is a good coach and a nice guy who knows the players very well.
“Then you have got Alan Kelly who is Preston North End through-and-through and does a great job with the keepers.”
Neil will meet the media on Wednesday and officially take up the post on Thursday, with him having a watching brief at Bamber Bridge on Friday.