Ryan Ross, from Belfast, was undergoing chemotherapy but came down with an infection that the youngster could not fight.
According to Belfast Live, Ryan was a huge Chelsea fan along with his dad, Gary.
Writing on official club paper, Terry, who lives in Surrey, wrote to the family to express his "great sadness" over Ryan's death and added it was "our privilege to play for fans like Ryan who are the life and soul of our club."
Dad Gary, 42, who works for George Best Belfast City Airport, said: "I just want to thank everyone who has shown their support to our family at this sad time.
"The loss of our son Ryan has touched the world and his favourite football team Chelsea sent this to letter to us."
East Belfast resident Ryan died at the Royal Victoria Hospital on Sunday (March 20) after suffering two heart attacks.
According to dad Gary, 42, his son fell victim to an infection which doctors could not prevent causing death.
Ryan had been diagnosed a year earlier and was put on a drugs and treatment trial that was due to last three years.