The former Wolves' striker claimed the first hat-trick of his Parkhead career in the 5-0 home thrashing of Inverness Caley Thistle on Saturday to take his tally to four goals in just four starts for the Hoops.
Now Celtic strike legend McGarvey is tipping Griffiths to provide the goals needed to fire up the Bhoys' European challenge later in the summer - and help the Parkhead faithful forget all about the departure of the prolific Gary Hooper.
McGarvey said: "I have long been a fan of Griffiths and I was delighted when Celtic signed him. For me, he is the 20-goal plus per season striker that a club of Celtic's magnitude should always have.
"The other huge plus for Celtic is that he has hit the ground running since he arrived in the window by getting his opening goal early.
"To score your first hat-trick in just your fourth start is impressive by any standards.
"So for me he has pretty much made the main striker's role his own."
McGarvey added: "But you know Leigh won't just supply goals for Celtic he will also help set up the likes of Anthony Stokes.
"But I like the fact that Griffiths can make a yard for himself with his movement, with the shot he has, that equals a lot of goals for Celtic."
The news of Griffiths' arrival at Parkhead at the end of the January transfer window was originally greeted with scepticism by sections of the Celtic support.
But McGarvey has every confidence that the Scotland striker can fill the goals void left by Gary Hooper's move to Norwich last summer.
The former Parkhead goal predator said: "When it comes to the Scottish Premiership there was never any doubt that Griffiths would score goals for Celtic.
"You only have to look at his record with Hibs and now he will benefit from a far superior service at Parkhead.
"When it comes to Europe then it is up to Leigh, but I believe he will score in the Champions League for Celtic.
"Can he replace Gary Hooper in that context? Well, we will know soon enough, I think there is every chance he can.
"But I have to say that Celtic were undermined by the departure of Gary Hooper. I believe Peter Lawwell got that one wrong.
"Enough money was taken in from selling Victor Wanyama and the one thing you don't do is sell your top goal scorer if you can avoid it."