(1) Background: Decellularized xenogeneic tissues are promising matrices for developing tissue-engineered cardiovascular grafts. In vitro recellularization of these tissues with stromal cells can provide a better in vivo remodelling and a lower thrombogenicity of the graft. The process of recellularization can be accelerated using a cultivation bioreactor simulating physiological conditions and stimuli. (2) Methods: Porcine pericardium was decellularized using a custom-built decellularization system with an optimized protocol. Autologous porcine adipose-derived stromal cells (PrASCs), isolated from the subcutaneous fat tissue, were used for recellularizing the decellularized pericardium. A custom cultivation bioreactor allowing the fixing of the decellularized tissue into a special cultivation chamber was created. The bioreactor maintained micro-perfusion and pulsatile pressure stimulation in order to promote the ingrowth of PrASCs inside the tissue and their differentiation. (3) Results: The dynamic cultivation promoted the ingrowth of cells into the decellularized tissue. Under static conditions, the cells penetrated only to the depth of 50 μm, whereas under dynamic conditions, the tissue was colonized up to 250 μm. The dynamic cultivation also supported the cell differentiation towards smooth muscle cells (SMCs). In order to ensure homogeneous cell colonization of the decellularized matrices, the bioreactor was designed to allow seeding of the cells from both sides of the tissue prior to the stimulation. In this case, the decellularized tissue was recolonized with cells within 5 days of dynamic cultivation. (4) Conclusions: Our newly designed dynamic bioreactor markedly accelerated the colonization of decellularized pericardium with ASCs and cell differentiation towards the SMC phenotype.