The 18-year-old striker goes straight into the Rams' squad to face Swansea on Saturday.
The France youth international will be looking to pick up valuable first-team experience during his time at Pride Park, while Derby boss Nigel Clough is hoping the youngster will add extra firepower to his front line.
"We've been monitoring the progress of Gilles for quite a while and it has been no secret we've been looking to get him to Derby County," Clough told the club's official website.
"It has taken a little while to get everything done, but we're delighted we've been able to secure a deal with Arsenal to bring him here.
"Gilles is still young and learning the game, so it is a great opportunity for him to develop and in turn we hope Derby County can benefit as well from having him with us."