And he hopes the signing will pave the way for Jackson to be joined by his former Perth team-mate Peter MacDonald.
The Ton boss had previously attempted to bring the one-time Republic of Ireland under-21 internationalist on loan in January, but failed to agree a financial package that suited both clubs.
But with Jackson, 23, having recently been released by the Perth side, Moore swooped to secure his services and add to his depleted frontline for next season.
Moore told the Tele: "I'm delighted to say we've signed Andy Jackson for next season.
"He's a player I've had my eye on for a while now, so we're very happy to have been able to bring him here.
"Like our other signings, he's signed a one-year deal, and I think that suits both sides, to be honest.
"We've also spoken to Peter MacDonald and he's away now to consider his options but he said he would get back to us so I'm waiting on that.
"He's certainly a good player and we're hoping that getting Andy on board will help us to get Peter too."
With or without MacDonald, Moore reckons the addition of Jackson represents a new weapon in the Ton armoury for the upcoming campaign.
He said: "Andy is a very ambitious boy who is confident in his ability.
"He's told me he wants to prove he can get goals at this level and believes he can score 15 goals-plus for us next season.
"And that's something I'd agree with. As long as we can supply him with the ammunition, he's the type of frontman who'll score you goals.
"He's a pest who plays on the shoulder of the last defender, makes intelligent runs and basically sniffs out goals.
"No offence to the boys we had here last season, but I believe he'll provide the cutting edge that we were missing.
"As I say, we've been trying to sign him for a while now, and I think our continued interest was a big part in his decision to come here, as he had some decent offers on the table from the likes of Ross County."
Moore also confirmed that released Hamilton stopper Andy Graham is due at Cappielow today to put pen to paper on his Morton contract.
And he says he expects to complete the formalities with Queen of the South midfielder Stephen McKenna shortly.
He said: "We've agreed a deal with Stephen and it's hopefully done and dusted now.
"He's on holiday just now but we're hoping to get him signed up when he comes back."