Biocompatible amphiphilic copolymers are attractive candidates for the fabrication of electrospun scaffolds to be used for tissue engineering and the delivery of biologically active compounds. The amphiphilic block copolymers poly(l-lactide)-b-poly(ethylene oxide)-b-poly(l-lactide) (PELA) and poly(l-lactide)-b-poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide)-b-poly(l-lactide) (PEPELA), which contain amorphous/crystalline and hydrophilic/hydrophobic blocks, were synthesized by ring-opening polymerization, and then electrospun to obtain non-woven fibrous scaffolds. Acetaminophen (AC) and celecoxib (CL) were used as hydrophilic and hydrophobic model drugs, respectively, to prepare drug-loaded scaffolds. The pure and drug-loaded scaffolds present a morphology characterized by randomly oriented fibres with integrated beads. The drug encapsulation and release profiles were determined by ultraviolet-visible spectroscopy. Due to the amphiphilic nature of PELA and PEPELA, both hydrophilic and hydrophobic drugs could be entrapped within the polymeric scaffolds, allowing the design of drug-delivery systems for specific applications. The combination of confocal Raman spectroscopy mapping and dynamic mechanical analysis revealed that the AC drug is preferentially maintained in the PEO phase, while the CL drug is fractionated between polyether and polyester phases and distributed throughout the fibrous structure due to its hydrophobic character.