A vascular graft that includes a biodegradable polyester electrospun tubular core; a biodegradable polyester outer sheath surrounding the biodegradable polyester tubular core; and a biodegradable poly(lactide) copolymer adhesive composition (i) disposed between the polyester electrospun tubular core and the polyester outer sheath, (ii) disposed between the polyester electrospun tubular core and the polyester outer sheath and on an outer surface of the of the polyester outer sheath, (iii) or disposed on an outer surface of the polyester outer sheath.