The 22-year-old striker has joined the Buddies on an 18-month deal from the Auckland-based outfit, with whom the Paisley club announced a strategic partnership with last year.
Greive, who was part of the New Zealand Olympic Provisional squad for the Tokyo 2021 Olympic Games, scored 25 goals in 33 appearances last year – including three hat-tricks in a row.
His performances earned him a place in the ISPS Handa Men’s Premiership ‘Team of the Season’ as well as being named the regional MVP (Northern League) in the New Zealand National League.
Saints boss Goodwin believes Greive will offer something different to the attacking players he currently has at his disposal and he is in line to make his debut against Dundee United this evening.
He said: “We are delighted to have another addition to the squad at the top end of the pitch.
“Alex is one we have been working with for the last wee while but couldn’t get him registered until the January window opened up.
“He’s brings creativity, he’s a little bit different to some of the other strikers we have at the moment, he’s quite dynamic and he’s a decent footballer so we’re excited to have him involved.
“He’s a very good professional. He’s looked very sharp in training and I think he’s surprised one or two.
“With the extra couple of squad members we can include in the match day squad, Alex might find himself involved tonight.”
Meanwhile, St Mirren talisman Jamie McGrath has turned down a pre-contract move to Aberdeen, with the midfielder reportedly exploring options south of the border.
The Republic of Ireland international is out of contract in the summer and is free to talk to other clubs this month, with Goodwin confirming he is resigned to losing his star man.
The Dons had approached McGrath and offered him terms to head north but the 25-year-old stalled on committing his future and is now likely to head down south.
Championship side Birmingham City and League One outfit Wigan Athletic are both believed to be willing to pay Saints £350,000 valuation of the player.