Armstrong began his career at Bury and joined the Blades for £100,000 in 2003.
He is expected to make his debut against Crystal Palace at the Madejski Stadium on Saturday.
Reading's Director of football Nicky Hammond added: "Chris is an experienced player who has made more than 200 senior appearances and competed in the top flight.
"We wish him the best of luck and are pleased to welcome him to the club."
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