Electrospun tissue-engineered grafts made of biodegradable materials have become a perspective search field in terms of vascular replacement, and more research is required to describe their in vivo transformation. This study aimed to give a detailed observation of hemodynamic and structural properties of electrospun, monolayered poly-ε-caprolactone (PCL) grafts in an in vivo experiment using a rat aorta replacement model at 10, 30, 60 and 90 implantation days. It was shown using ultrasound diagnostic and X-ray tomography that PCL grafts maintain patency throughout the entire follow-up period, without stenosis or thrombosis. Vascular compliance, assessed by the resistance index (RI), remains at the stable level from the 10th to the 90th day. A histological study using hematoxylin-eosin (H&E), von Kossa and Russell–Movat pentachrome staining demonstrated the dynamics of tissue response to the implant. By the 10th day, an endothelial monolayer was forming on the graft luminal surface, followed by the gradual growth and compaction of the neointima up to the 90th day. The intense inflammatory cellular reaction observed on the 10th day in the thickness of the scaffold was changed by the fibroblast and myofibroblast penetration by the 30th day. The cellularity maximum was reached on the 60th day, but by the 90th day the cellularity significantly (p = 0.02) decreased. From the 60th day, in some samples, the calcium phosphate depositions were revealed at the scaffold-neointima interface. Scanning electron microscopy showed that the scaffolds retained their fibrillar structure up to the 90th day. Thus, we have shown that the advantages of PCL scaffolds are excellent endothelialization and good surgical outcome. The disadvantages include their slow biodegradation, ineffective cellularization, and risks for mineralization and intimal hyperplasia.