A requirement for achieving sustainable concrete structures is to develop a quantitative method for designing concrete mixtures that yields the target rheological properties and compressive strength. Toward this objective, this paper proposes a mathematical model approach to improve the sustainability of the concrete industry. A postulation that packing density, a function of the concrete mixture, provides the link between concrete mixture, rheological properties, and compressive strength was investigated. Rheological models for yield stress and plastic viscosity, and a compressive strength model were adopted with packing density as a central variable. The rheological models employ a cell description that is representative of fresh concrete. The compressive strength model is based on excess paste theory to account for the concrete mixture proportions, gradation of aggregate particles, and porosity. An experimental program was developed to calibrate and test these models. Results revealed that packing density provides a consistent and reliable link, and that the concrete mixture composition can be designed to achieve the target rheological properties and hardened properties and ensure quality control. Consequently, a new mixture proportioning methodology was developed and proposed as an improvement to the ACI 211.1 mixture design method. Furthermore, a case study was conducted to test for the applicability and adequacy of this proposed method. This research outcome, which provides a quantitative approach to design concrete mixtures to meet specific strength requirements and rheology, can also be used to ensure quality control before concrete is cast.