Gaston, 25, was a key player for Rovers last term as the Cliftonhill club avoided relegation to the Third Division via the play-offs after a penalty shoot-out with Stranraer.
The highly-regarded goalkeeper was also on the radar of Rangers two years ago and will formally complete his move to Cappielow next Monday.
Moore has backed Gaston to show his class with his new club, and believes the move solves an issue that dogged Ton last season.
Moore told the Telegraph: "Derek has agreed to sign.
"We have got his papers sorted now although they don't get lodged until the start of pre-season on the 25th.
"To be honest I made a mistake last year in not getting somebody in to back up big Colin Stewart, we only had big Matty McGinley in and he was straight from the Juniors.
"I don't think Matty was quite ready. But I have been to watch Derek in the play-offs against Stranraer and I was impressed with him.
"He was close to a big move a couple of years ago with Rangers taking a look at him and we are sure he is ready for the step up.
"Derek is a good shot-stopper, he looks a bit awkward but he kicks the ball really well. When I watched him against Stranraer he kicked the ball on to their striker's head every time.
"He maybe needs to work on commanding his box with his talking, but hopefully he can come on board and kick on with us.
"We've got two more added to the squad now and at the end of the day it's now down to us to fill in the rest of the pieces."
The Ton boss has also strengthened the other end of his team, with MacDonald agreeing terms on a new one-year contract.
The 31-year-old finished top scorer at Cappielow last season after netting 15 times and his decision to remain in Greenock is a boon for Moore.
He said: "We've got Peter MacDonald back on board again - good strikers are hard to come by so I'm delighted with that.
"He was top scorer for us last season, although at the time I always felt he could score a few more goals for us.
"But then in fairness I don't think we really gave him much ammunition to work with sometimes so that was maybe unfair.
"We are delighted he has signed - we've now got him, big Peter Weatherson and wee Archie Campbell up front."