The vastly-experienced coach has taken over following the resignation of Gary Hargreaves and Scott Somerside, the pair who secured the club's first-ever Premier Division title last season.
Norrie will be assisted by former Lancaster City player Michael Yates while, in a summer of change for Garstang, Adrian Wilding will return as chairman with Les Taylor helping on the commercial side.
Norrie has worked at a host of clubs including Dundee, Gretna, Morecambe, Lancaster City and latterly at Carnforth Rangers and Trimpell.
He said: "To win back-to-back championships is hard at any level but my job is to keep them challenging. We will see if the players have got the desire to go and win it again.
"They (Hargreaves and Somerside) have done an exemplary job at Garstang and my job is to progress their good work. It is a hard act to follow."
Norrie was keen to link up with Mr Wilding and Mr Taylor, who has extensive experience at Blackpool, Morecambe, Lancaster City and Fleetwood.
"They have got ideas of progression and that appeals to me. There are a lot of hard-working people there and you need that at this level," he said.
Norrie took his first training session on Tuesday last week and does not envisage making many changes.
"If something is not broke, you don't try to fix it," he said.
There was unlikely to be many players following him from Trimpell, the Morecambe-based side where Norrie has spent the past three seasons, winning promotion in what was the club's first year back in the league.
They have twice since just missed out on promotion to the Premier Division, also reaching the cup semi-finals.
Norrie said: "I had three great years at Trimpell but I had taken them as far as I could."
Yates has been playing with Norrie at Trimpell. He is also a coach at Liverpool FC's Academy.