Cuthbert, a star performer in the Test match arena this year, rejected offers from other clubs in committing his future at the Arms Park.
"I had a lot of decisions to make, but I am glad I've got it sorted and this is the place I want to be to take my rugby career forward," Cuthbert, 22, said."I did have some good offers from other clubs, but I wanted to stay with the Blues."
His decision has also bucked the trend of top Wales players moving to France, with Jamie Roberts and Dan Lydiate both set to join the exodus next season.
Mike Phillips, Gethin Jenkins, James Hook and Luke Charteris already play in the French Top 14, while prop Paul James is in his first season at Aviva Premiership club Bath.
"I've certainly seen the progress on the pitch, although we may not be getting the results right now," Cuthbert added. "We are just losing by narrow margins, and you can tell it's coming.
"Hopefully, we will get some quality players in next season and those close losses will turn into wins for us."
Cuthbert scored tries against Scotland, Italy and France during last season's RBS Six Nations title and Grand Slam-winning campaign, and he transferred that form into the recent autumn Tests, claiming a try against New Zealand.
Blues rugby director Phil Davies said: "Alex is 22. He has a fantastic future ahead of him, not just at the Blues but in the game in general. He is a vital part of our squad.
"Alex is s a great try-scorer, but he is still young and developing all the time. His work-rate is phenomenal and his defence and reading of the game is improving considerably. Hopefully, he will get better and better over the next three years."