Ruthenium complexes have been widely studied as potential alternatives to platinum-type anticancer drugs due to their unique medical properties such as high selectivity, strong ability to inhibit solid tumour metastasis. However, non-specific biodistribution, and weak lethality of ruthenium to cancer cells limit its use in medical application. Drug delivery systems offer the ability to integrate multiple drugs in one system, which is particularly important to enhance the chemotherapeutic efficacy and to potentially achieve a synergistic effect of both drugs. Here, we report a dual drug nanocarrier that is based on a self-assembled biodegradable block copolymer, where the ruthenium complex (RAPTA-C) is chemically attached to the polymer chain, while another drug, paclitaxel (PTX), is entrapped in the core of the micelle. The dual drug delivery system was studied via in vitro tests using MDA-MB-231 breast cancer cells and it was observed that RAPTA-C in combination with PTX significantly enhanced anti-tumour and anti-metastasis activity.