The Gunners managed to get a deal over the line for the Scotland international on transfer deadline day following months of speculation surrounding the full-back.
Arsenal were reported to have agreed a deal worth around £25m for the Celtic left-back as Unai Emery managed to bolster his full-back options ahead of the new season.
Tierney is currently sidelined with an injury that he picked up at the start of the Scottish Premier League season.
Former Arsenal defender Winterburn is confident that Tierney won’t struggle to adapt to the north London side’s style of football and the Premier League.
“The Premier League is the most brutal league in the world, especially for defenders, but Kieran Tierney is a sensational signing and will have no problem settling in,” Winterburn told Sportingbet.
“He is a young player who has gained huge experience at Celtic, he has also played Champions League football so will be used to the quality of football.
“At the end of the day, I’m less worried about what a player has done before; I’m more interested in what happens when they come to your football club.
“Tierney fits the bill and is someone that will give Arsenal plenty of width and defensive skills down the left-hand side. He has been a player that Arsenal have courted for most of the transfer window, so I’m delighted that Arsenal have got the transfer over the line.”
Tierney netted eight times in 170 games over the past five seasons at the Scottish Premier League champions.
The 22-year-old has also represented Scotland on 12 previous occasions to get international experience under his belt.
Arsenal signed Brazilian teenager Gabriel Martinelli, Saint-Etienne defender William Saliba, Real Madrid midfielder Dani Ceballos, Lille winger Nicolas Pepe and Chelsea FC centre-half David Luiz this summer.
The Gunners were 1-0 winners against Newcastle United at St James’ Park in their Premier League opener last weekend courtesy of Pierre Emerick-Aubameyang’s second-half winner.
Arsenal will host Burnley in the Premier League at The Emirates on Saturday.
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