Quy will be supported by overseas Vietnamese Pham Ngoc Chu who is a member of the Hungarian Olympic Committee.
Chu, chairman of the Vietnam Business Association, will take care of Phuoc during his time there.
The three-time Southeast Asian Games winner will train with Shane Tusup, coach of world record holder Katinka Hosszu.
He will leave for Budapest in early February.
Quy, 22, has been plagued by injuries and training problems since 2012.
Quy said that with the right coaches and training, he could go far.
He said swimmers sometimes reached their peak at the age of 27, so he would be much better in the next few years.