The 23-year-old has moved to Fir Park for an undisclosed fee on a three-year contract after scoring 23 times in 37 starts for the Conference Premier side last season.
Moult started out at Stoke City and made three appearances for them as a teenager in the 2009/10 campaign.
After loans at Bradford, Mansfield (twice), Accrington and Alfreton, he joined Northampton then Nuneaton after a successful temporary spell.
He scored 17 times for them in the 2013/14 campaign and that led to his move to Wrexham, which saw him scored twice at Wembley in the FA Trophy final in March.
The Welsh side ultimately lost to North Ferriby United on penalties after a 3-3 draw but Moult made his mark and now Motherwell have made their move.
He told the official Motherwell website: “I’m delighted to be here. It is a massive step in my career and it wasn’t a move I could turn down.
“I’m here to score goals and hopefully I can do that. In two seasons I’ve scored 40 goals and I’m going to try and make that sixty in three, or even more if I can.
“I’ve had a look at the side and they play some fantastic attacking football. With two pacey wingers who like to link up with the frontmen, hopefully that will suit me and I can hit the ground running.”