The women, who were both in their 50s, were stabbed to death near the west coast city of Izmir last week.
The victims' bodies were released from a mortuary in Izmir on Monday and flown to Dublin Airport on Wednesday.
The hearses were accompanied by friends and family and the police on both sides of the border on their journey north.
Both funerals will be on Friday - Ms Graham's in Newry in the morning and Ms Dinsmore's in Warrenpoint in the afternoon.
Ms Graham's daughter Shannon arrived home on Monday night accompanied by her father.
In a statement earlier, St Mary's High School - which Shannon attended - said staff and pupils were "deeply saddened" by the tragic deaths.
"Our thoughts and prayers are with Shannon during this very difficult time," the statement said.
"As a school community we will ensure all the support is available to both Shannon and her peers as they begin a new academic year."
Shannon's Turkish boyfriend Recep Cetin has reportedly confessed to the double killing.
The suspect, also known as Alex, worked at a restaurant in the popular tourist resort of Kusadasi.
It is alleged that he confessed to killing Ms Graham and Ms Dinsmore, after being refused permission to marry Shannon.
The suspect is alleged to have taken Ms Dinsmore and Ms Graham to a secluded wooded area and murdered them there.
The friends were on holiday in Kusadasi, about 100km from Izmir.
Shannon was on a boat trip when the killings happened. She alerted police when she arrived home and could not get in touch with her mother.