Greening is a UEFA A licensed coach and has coached at Nottingham Forest and another of his former clubs, York City.
The 42-year-old, an unused substitute for Manchester United in the 1999 European Cup final said sentiment had played a big part in him applying for the job.
Darren Kelly resigned as manager of the Northern Premier League team, phoenix club to the one he followed as a child.
"The fact that Scarborough is my home town is 100 per cent the reason that I put in for the job," he said.
"I have applied for it two or three times before and when Daz left I received a few calls asking if I'd sent my CV over.
"I thought, why don't I give this one more crack and I was surprised to be offered the chance to meet up.
"It is a very nice fit for me. I was a fan and a ball boy at Scarborough FC, I used to walk down Seamer Road with my dad and my brothers, stopping off at the pub, drinking Coke and eating crisps.
"I have great memories of it and now I am looking forward to what the future holds.
"I want to excite our supporters and I want to get the younger generation off their Xboxes and PlayStations and down to the Flamingo Land Stadium.
"I want my players to play, not only for me, but for the town of Scarborough."
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