Godden, 24, joined the Fleet from Scunthorpe in 2014 and scored 30 goals in National League South last season.
"I dropped down to Ebbsfleet to rejuvenate and get regular football," said Godden, who has joined on a free.
"The main aim was to bounce back and make a name for myself in the Football League and I thank Darren Sarll and Stevenage for this opportunity."
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Ebbsfleet striker Matt Godden has become Darren Sarll's first signing as full-time manager of Stevenage.