The Gunners decided to appoint the former Paris Saint-Germain and Sevilla manager as Arsene Wenger’s replacement at the end of the 2017-18 Premier League season.
The Spanish head coach wasted no time exerting his influence at the north London side following the addition of five new players in the summer transfer window.
The new Arsenal manager made an underwhelming start to his reign after a 2-0 loss to defending Premier League champions Manchester City followed by a 3-2 defeat by Chelsea FC at Stamford Bridge in August.
However, the Gunners have bounced back from those early defeats with six successive top-flight victories to hoist themselves up to fourth place in the Premier League table.
Arsenal have eased to victories over Fulham, Watford, Everton, Newcastle United, Cardiff City and West Ham United to move to within two points of Premier League leaders Manchester City.
Former Gunners striker Wright has enjoyed the north London side’s sequence of results but the retired England international warned the Gunners that there are tougher tests on the horizon.
“Tougher tests lie ahead, naturally, and the next couple of months in which they play Liverpool, Wolves, Spurs and United will tell us lots,” Wright told The Sun.
“Past experience shows that if they lose a couple of them, the critics will be on Arsenal like a ton of bricks.
“But it is easier to go into a run like that with the confidence and momentum that winning brings.
“So I would tell everyone to enjoy the ride and hope it does not slow down just yet.”
Arsenal will take on Leicester City in their next Premier League fixture at The Emirates after the international break following a 5-1 rout of Fulham at Craven Cottage.
The Gunners will take on Portuguese giants Sporting Lisbon at Estadio Jose Alvalade in the Europa League at the end of October in their third Europa League group-stage fixture.
The north London side will host Sporting Lisbon in the reverse fixture at The Emirates before the Gunners welcome Liverpool FC to north London at the start of November.
Emery arrived at Arsenal with a rich pedigree in the Europa League after winning the competition on three previous occasions with Sevilla.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news