In this paper, a general transformation of binary linear block codes (BLBCs) to (possibly, multi-kernel) polar codes with dynamic frozen bits is proposed. Through a simple matrix permutation operation, a one-to-one connection between the codewords of a BLBC and its transformed polar code can be established. This transformation allows the usage of any decoding algorithm of polar codes for efficient soft decoding of BLBCs, including the powerful successive cancellation list (SCL) decoding algorithm. Simulations show that the soft SCL polar decoding of BLBCs can achieve a comparative performance to the order statistic decoding (OSD), as well as the maximum-likelihood decoding (MLD) in certain cases, with a much lower computational complexity.