This paper proposes joint user association and energy-efficient resource allocation in the uplink of multi-user two-tier Orthogonal Frequency Division Multiplexing (OFDM) Heterogeneous Networks (HetNets) subject to user's maximum transmission power and minimum-rate constraints. The proposed scheme aims at achieving high rates at low powers satisfying the user's quality-of-service (QoS) constraints (in terms of minimumrate requirements) by offloading the users with low signal to noise ratio (SNR) from macrocell to the pico base station (BS). A channel-to-noise-ratio (CNR)-based rate proportional resource allocation approach is proposed to transform the minimumrate constraint into a minimum required transmission power constraint on each subcarrier. The single-user single-carrier and multi-user multi-carrier energy efficiency (EE) maximization problems are then solved under maximum and minimum power constraints using Karush-Kuhn-Tucker (KKT) conditions. The impact of users' maximum transmission power and minimumrate requirements on EE and throughput are investigated through illustrative results. The rate-proportional approach is evaluated against the equal rate allocation approach for different user associations and various numbers of users, maximum transmission power, and circuit powers. Significant gains in EE can be achieved for the HetNets if the path loss based user association is combined with the proposed CNR rate proportional mechanism.