Collins, 20, twice won the FA Youth Cup with Chelsea and lifted the UEFA Youth League in 2016.
"I'm delighted to have this opportunity coming from Chelsea Under-23s now to play men's football," Collins told the club website.
"Bradley joining Forest Green Rovers shows how far we've come," the League Two side's boss Mark Cooper added.
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Forest Green Rovers have signed goalkeeper Bradley Collins on a season-long loan deal from Chelsea.