Morrison, 21, is back at the club for a second spell, having signed in 2016 on a youth loan.
He was the second striker signed last week after Brodie Litchfield, who struck a hat-trick the previous Saturday in the 5-2 win at Bottesford Town, also agreed to join.
Assistant manager Ross Hannah said of Morrison: “Curtis is somebody we had an eye on at the end of last season when he was in the league above at Guiseley.
“He did well on the occasions we watched him, but for one reason or another he didn’t get a fair chance and we were surprised to see him released from there.
“We were pleased though, as it gave us an opportunity to speak to him and get him in with us.
“He’s had a successful trial. He brings pace, power, good athleticism and will terrorise defenders with those attributes wherever he plays.
“We’re looking forward to working with him and helping him develop as we believe he’s still young enough and has the potential to kick on — hopefully that’s with us this season.”
Morrison has previous experience at Chesterfield and Matlock Town as well as Guiseley.
Litchfield, who was recently in the National League North at FC United of Manchester, said: “Goals and assists are obviously important to me, but the ultimate has to be helping the team back up into the Conference, as that’s where I want to be.
“With the side we have here that’s got to be possible.”
Manager Liam King said: “Brodie has been a player who has come in and impressed in pre-season and fully deserves to be offered a deal.
“He is a young lad who is hungry to do well in the game, and we look forward to helping him achieve his potential.”