Mr Durkan has spoken frequently about his sister, Gay (28) who was a nurse at Altnagelvin hospital.
The “Gabrielle Award” has been established to mark the tenth anniversary of her death this weekend.
Ms Durkan was also a niece of former SDLP leader and Foyle MP Mark Durkan.
A spokeswoman for RCN Northern Ireland said the one-off bursary would be available to pre-registration nursing students at Queen’s University, Ulster University or the Open University (Northern Ireland).
Sponsored by Ms Durkan’s sisters, Mary and Isobel, the award will provide student nurses with the opportunity to explore a particular aspect of healthcare further.
The spokeswoman said: “It can be used to fund travel, attendance at a conference, developing a shadowing experience or another option that supports their topic of choice.”
Mary Durkan said the award was a fitting tribute to her sister’s life and legacy and was a “timely nod” to the ongoing work of nurses in the most challenging of circumstances.
Ms Durkan said it was also an acknowledgement of the pressures facing students and student nurses and recognition of the important role of trades unions.
The former Derry and Strabane councillor said: “I’m delighted that RCN Northern Ireland has launched a special one-off bursary scheme for student nurses in memory of our Gay.
“Thanks too to NUS-USI (National Union of Students-Union of Students in Ireland), Queen’s University Students’ Union and Ulster Uni Students’ Union for their support for the Gabrielle Award.”
Foyle MLA Mr Durkan said he was pleased that student nurses would benefit from his sister’s memory.
The scheme, will offer a number of small bursaries to nursing students, details of which are available through their schools of nursing.