Blackett played 12 times for United's first-team after making his debut under former Red Devils boss Louis Van Gaal.
The 22-year-old also spent time out on loan at Celtic, Birmingham City and Blackpool.
Former Manchester United defender and Reading manager Jaap Stam hailed his new signing.
"As we know, Tyler is a talented defender who has played for United's first team," he told Reading's official website.
"He can play as a left-back or a left-sided centre-back; he has got great potential in the sense that he is quick and athletic, defensively he is strong and he is good at set-pieces.
"As a defender he can go and play high up the pitch as well, and that is what we need in the squad".