Moli spent last season playing in France with Epinal, but has been training with Boro during the summer and scored in the friendly against Rushall Olympic.
He said: "It's good to be here. I like the set up and I want to play games and score goals for the club."
Moli, who moved to Liverpool when he was aged just 14 from Luton Town for an undisclosed fee before going on to have spells with Wolves, Boreham Wood, Hayes & Yeading United, New Radiant in the Maldives and Bedford Town, is a player that Boro boss Kevin Wilson has been tracking for some time. He said: "I tried to sign David for the Boro last summer, but we couldn't get the deal over the line back then.
"I'm delighted to have got him this time around. He has a great pedigree, but needs to knuckle down now and show everyone what we know he can do. He's a natural goal scorer and I'm looking forward to working with him".