There is no way to answer your structural question. What are the loads, roof size and materials?, Do you need to consider snow?. What is the overhang distance and size of lumber? Do you have alternatives?
It sounds like you are connecting a shed extension to the eaves of an existing roof. Could you instead construct a gable that ties into the roof (jack rafters and valley flashing). This arrangement would generally look better, and would be a much more leak-proof and stronger system.