The Belarus international must yet complete a medical and obtain a work permit but is set to become Arsene Wenger's first signing of the summer as he looks to prise the Premiership trophy back from London rivals Chelsea.
After a disappointing league and European campaign Wenger had been keen to add more experience to a midfield that relied heavily on inexperienced talent Francesc Fabregas last year.
The versatile Hleb has made over 130 appearances with Stuttgart in a career spanning five years in Germany, and has emerged as one of Die Bundesliga's most promising talents.
After having an initial offer turned down Wenger has now captured his man and beaten the likes of Barcelona, Real Madrid and Chelsea in concluding his lengthy pursuit of the player.
Wenger voiced his delight at the signing of the 24-year-old, who could rival Freddie Ljungberg for the right-hand side of midfield, and expressed a hope that he could prove a valuable player for The Gunners.
"We are delighted that Alexander Hleb has agreed to join us," Wenger told the club's official website.
"He is a player I have admired for some time now and I know he will provide our squad with great quality.
"Hleb has proved his ability with his performances in the Bundesliga in recent seasons and he definitely has the potential to do very well with Arsenal."
Hleb himself was excited at the prospect of joining the likes of Thierry Henry and Dennis Bergkamp at the FA Cup winners.
"I am very happy to have this fantastic opportunity to join Arsenal. They are a club with a great history and many world class players," said Hleb
I've managed to see him on EuroSport a few times, watch out for him, he is quality!
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