The success of implant treatment is dependent on the osseointegration of the implant. The main goal of this work was to improve the biofunctionality of the Ti-13Nb-13Zr implant alloy by the production of oxide nanotubes (ONTs) layers for better anchoring in the bone and use as an intelligent carrier in drug delivery systems. Anodization of the Ti-13Nb-13Zr alloy was carried out in 0.5% HF, 1 M (NH4)2SO4 + 2% NH4F, and 1 M ethylene glycol + 4 wt.% NH4F electrolytes. Physicochemical characteristics of ONTs were performed by high-resolution electron microscopy (HREM), X-ray photoelectron spectroscopy (XPS), and scanning Kelvin probe (SKP). Water contact angle studies were conducted using the sitting airdrop method. In vitro biological properties and release kinetics of ibuprofen were investigated. The results of TEM and XPS studies confirmed the formation of the single-walled ONTs of three generations on the bi-phase (α + β) Ti-13Nb-13Zr alloy. The ONTs were composed of oxides of the alloying elements. The proposed surface modification method ensured good hemolytic properties, no cytotoxity for L-929 mouse cells, good adhesion, increased surface wettability, and improved athrombogenic properties of the Ti-13Nb-13Zr alloy. Nanotubular surfaces allowed ibuprofen to be released from the polymer matrix according to the Gallagher–Corrigan model.