It was confirmed today the 22-year-old will play no further part in the competition and has been replaced by Morgan, who has made one appearance in the GUINNESS PRO12 this season.
Morgan tweeted: "Massively gutted for Cory with his injury, but hugely honoured to be called up into the World Cup squad. Exciting week ahead in London."
Allen also took to Twitter following the news, saying: "Thanks for all the messages. Gutted to be taking no further part in this year's RWC but it was fun while it lasted!"
Morgan has made 16 appearances in the GUINNESS PRO12 since making his debut during the 2013/14 campaign.
The 20-year-old's performances last season resulted in his first cap for Wales, which came during the 35-21 defeat to Ireland in August.
Wales head coach Warren Gatland said: "It's disappointing to lose Cory in this way, especially following his man-of-the-match display against Uruguay.
"Tyler was part of our extended squad and trained very well and will link up with us in London."
Allen is one of many who have suffered injuries in Wales' opening World Cup game or in the build-up to the competition.
Jonathan Davies, Leigh Halfpenny and Rhys Webb were ruled out before the tournament began, and GUINNESS PRO12 quartet Samson Lee, Paul James, Dan Lydiate and Aaron Jarvis also picked up injuries at the weekend.
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Guinness PRO12 Blues News
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