Armstead was signed by the Patriots last year from the CFL, where he had played one season for the Toronto Argonauts as he missed the NFL Draft in 2012 after having a heart attack while with the USC Trojans.
The defensive tackle failed to play a game for Bill Belichick's side as he sustained an infection last year during training camp and was placed on the non-football injury list.
Armstead has now taken the decision to retire a week before his side are due to start their training camp for the 2014 season.
Belichick told the club's official website: "It has been a pleasure being around Armond, as he gave everything he could to play for us. Armond worked extremely hard since joining us last February.
"He's had a lot of adversity personally that he's had to deal with – unusual compared to most other players – but he's always had a great attitude, worked hard and really did everything we asked him to do.
"While it is unfortunate he will not be able to play football, Armond is an outstanding young man who has a very bright future in whatever path he chooses."
The Patriots open the 2014 NFL season against the Miami Dolphins on September 7.