There will also be a minute's silence before the Worthington Cup tie at Highbury.
The 56-year-old collapsed with a brain haemorrhage at the club's training ground in Hertfordshire while taking a coaching session on Tuesday.
He was taken to nearby Hemel Hempstead hospital and put on a life-support machine but died in the early hours of Wednesday.
He was also famous for his exploits during Arsenal's double-winning season of 1970-71.
The club's official website described him as "a kind, warm-hearted man" and "an inspiring coach as well as a superb player".
The Arsenal team will wear black armbands for Wednesday evening's home match with Ipswich.
There will also be a minute's silence before the Worthington Cup tie at Highbury.
Armstrong played every game of Arsenal's double-winning triumph 20 seasons ago, and also held the club's appearance record before it was passed by David O'Leary and Tony Adams.
One of the unsung heroes of the 1970-71 side, he was an old-fashioned winger who could operate on both flanks and also scored goals.
Former team-mate George Graham brought him back to Highbury in 1990 while the Scot was Arsenal manager.
Graham, now in charge at Spurs, said he was "devastated" by the death of the man known as "Geordie".
"It is extremely sad and a terrible shock," he said.
"He was such a thorough professional and a great help to me at Arsenal. As soon as I knew he was available when he was out in the Middle East I jumped at the chance to bring him back."
Frank McLintock, captain of the double-winning side, said: "This has shattered me because I can honestly not remember George having a day's illness all the time I knew him.
"If he ever had to miss an Arsenal game through injury he was absolutely heartbroken. He lived for the game but he was also a great family man as well."
Armstrong leaves a wife Marje and a son and daughter.