Gloucester are currently without a win in the Prem this season having lost their first five matches of the campaign.
They have conceded 190 points – only bottom-of-the-table Newcastle Red Bulls have conceded more.
Gloucester said Mitchell will focus on “improving tackle and collision effectiveness” within the team’s “overall defensive development”.
He was named World Rugby’s coach of the year following England’s win at Twickenham, having also guided the Red Roses to a fourth consecutive Six Nations Grand Slam and seventh straight title in April.
He also worked as head coach of Sale Sharks in the 1990s and has held roles in the United States, Australia, South Africa and Japan.
Gloucester next play Bath in the Prem Rugby Cup on Friday, 14 November before returning to league action at home to Harlequins on Saturday, 29 November.
