The region is now able to confirm that, following screening and testing, Matthew has been given the all clear by specialists and does not require further medical treatment.
Matthew will now start a full-time training programme at Blues as he regains his match fitness with a view to return to rugby.
"It is a massive weight off my shoulders and while there has always been light at the end of the tunnel for me during difficult times this is the news I always wanted to hear," said Rees.
"Now I've been given the all clear I can concentrate on getting back to match fitness and hopefully I can play a part towards the end of this season for the Blues.
"I've been truly overwhelmed by the good luck messages I have received from the rugby world and the fantastic support I've had from my friends, family, my team-mates and staff at Cardiff Blues and the WRU throughout my treatment. It has meant a huge amount to me.
"I also want to pay a special thank you to everyone at Velindre Hospital in Cardiff, in particular the specialists and nurses on the Princess Margaret Ward for everything they have done for me."
Matthew also paid tribute to supporters and sponsors who have raised over £15,000 for the Velindre Hospital through donations and by purchasing 'Smile For Your Captain' wristbands.
"It's been fantastic to see so much money raised and really humbling for me," added Rees.
"So much positive awareness has been raised and a large sum of money will now go to the inspiring and life-changing work of the Velindre Hospital."
Director of Rugby Phil Davies said: "On behalf of all the players, coaches and staff at the Blues, we are absolutely delighted for Matthew that he's come through this ordeal. He has shown an amazing resilience and mental toughness throughout such a difficult time.
"Matthew has continued to train, with our strength and conditioning staff throughout his treatment, which is testament to his strength of character and ability to overcome adversity. Not many people could have done that while remaining so positive and determined.
"We are all now all looking forward to seeing him back on the training field and on the field in a Cardiff Blues jersey in the future. This news is a massive boost to everyone, but nobody more than Matthew and his family."
It's not too late to show your support for Velindre Hospital in Cardiff. Donate by clicking on www.justgiving.com/Cardiff-Blues