Biodegradable block and random copolymers have attracted numerous research interests in different areas, due to their capability to provide a broad range of properties. In this paper, an efficient strategy has been reported for preparing biodegradable PCL-PLA copolymers with improved thermal, mechanical and rheological properties. Two block-copolymers are synthesized by sequential addition of the cyclic esters lactide (L-LA or D,L-LA) and ε-caprolactone (CL) in presence of a dimethyl(salicylaldiminato)aluminium compound. The random copolymer of L-LA and CL was synthetized by using the same catalyst. Chain structure, molar mass, thermal, rheological and mechanical properties are characterized by NMR, SEC, TGA, DSC, Rheometry and DMTA. Experimental results show that by changing the stereochemistry and monomer distribution of the copolymers it is possible to obtain a variety of properties. Promising shape-memory properties are also observed in the di-block copolymers characterized by the co-crystallization of CL and L-LA segments. These materials show great potential to substitute oil-based polymers for packaging, electronics, and medicine applications.