The League One club have been forced into the transfer market after regular stopper Stephen Bywater was ruled out for at least a month with a shoulder injury.
That has resulted in Burton moving for 21-year-old Collins, who made 45 appearances for Forest Green Rovers during the last campaign.
Manager Nigel Clough told the club's official website: "We are still awaiting scan results for Stephen but at the moment we are thinking anywhere between four and eight weeks, so we have chosen a good young Chelsea keeper who had good experience out on loan last year with Forest Green.
"I spoke to Mark Cooper (Forest Green manager) about him and he recommended him and said he really grew up in his time there last season. By the end of the loan spell, he had become more of a man by playing in League Two and he will start on Saturday."
Collins was involved in Chelsea's first-team squad during pre-season but was largely kept in reserve.