The former flanker, on the coaching staff at Saracens since 2008, did not win any international caps but did play for England in a non-cap match against the United States in the run-up to the 1999 World Cup.
He has been widely credited with turning Saracens into one of the best defensive sides in Europe.
"An important part of England going forward is to make sure we keep the traditional and fundamental bits of English rugby in place and that has always been a strong set piece and a very aggressive defence," Australian Jones said in an RFU statement.
"He (Gustard) has overseen Saracens growth as a team. He has produced an aggressive defence system there and we are hoping he can do the same for England.”
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England's first game under Jones is away to Scotland in the Six Nations Championship on Feb. 6.
Jones will start with a new management set-up after former coach Stuart Lancaster's assistants' Graham Rowntree, Andy Farrell and Mike Catt were released on Monday.
Lancaster left "by mutual consent" last month in the wake of England's pool-stage exit from the Rugby World Cup on home soil.
Former England captain Steve Borthwick, who worked as a forwards coach with Jones when he was in charge of Japan, is expected to link up with the Australian again.
However, the move appears to have hit a snag with his club Bristol saying they have not yet agreed to release him.
(Writing by Justin Palmer; Editing by Ken Ferris)
