The design and study of efficient polymer-based drug delivery systems for the controlled release of anticancer drugs is one of the pillars of nanomedicine. The fight against metastatic and invasive cancers demands therapeutic candidates with increased and selective toxicity towards malignant cells, long-term activity and reduced side effects. In this sense, polyphosphazene nanocarriers were synthesized for the sustained release of the anticancer drugs camptothecin (CPT) and epirubicin (EPI). Linear poly(dichloro)phosphazene was modified with lipophilic tocopherol or testosterone glycinate, with antioxidant and antitumor activity, and with hydrophilic Jeffamine M1000 to obtain different polyphosphazene nanocarriers. It allowed us to encapsulate the lipophilic CPT and the more hydrophilic EPI. The encapsulation process was carried out via solvent exchange/precipitation, attaining a 9.2–13.6 wt% of CPT and 0.3–2.4 wt% of EPI. CPT-loaded polyphosphazenes formed 140–200 nm aggregates in simulated body physiological conditions (PBS, pH 7.4), resulting in an 80–100-fold increase of CPT solubility. EPI-loaded polyphosphazenes formed 250 nm aggregates in an aqueous medium. CPT and EPI release (PBS, pH 7.4, 37 °C) was monitored for 202 h, being almost linear during the first 8 h. The slow release of testosterone and tocopherol was also sustained for 150 h in PBS (pH 7.4 and 6.0) at 37 °C. The co-delivery of testosterone or tocopherol and the anticancer drugs from the nanocarriers was expected. Cells of the human breast cancer cell line MCF-7 demonstrated good uptake of anticancer-drug-loaded nanocarriers after 6 h. Similarly, MCF-7 spheroids showed good uptake of the anticancer-drug-loaded aggregates after 72 h. Almost all anticancer-drug-loaded polyphosphazenes exhibited similar or superior toxicity against MCF-7 cells and spheroids when compared to raw anticancer drugs. Additionally, cell-cycle arrest in the G2/M phase was increased in response to the drug-loaded nanocarriers. Almost no toxicity of anticancer-drug-loaded aggregates against primary human lung fibroblasts was observed. Furthermore, the aggregates displayed no hemolytic activity, which is in contrast to the parent anticancer drugs. Consequently, synthesized polyphosphazene-based nanocarriers might be potential nanomedicines for chemotherapy.