The main implementation impairments degrading the performance of direct-conversion radio transmitters are in-phase/quadrature (I/Q) mismatch, local oscillator (LO) leakage, and power amplifier (PA) nonlinear distortion. In this article, we propose a recursive least-squares-based learning algorithm for joint digital predistortion (PD) of frequency-dependent PA and I/Q modulator impairments. The predistorter is composed of a parallel connection of two parallel Hammerstein (PH) predistorters and an LO leakage compensator, yielding a predistorter which as a whole is fully linear in the parameters. In the parameter estimation stage, proper feedback signal from the transmitter radio frequency (RF) stage back to the digital parts is deployed, combined with the indirect learning architecture and recursive least-squares training. The proposed structure is one of the first techniques to explicitly consider the joint estimation and mitigation of frequency-dependent PA and I/Q modulator impairments. Extensive simulation and measurement analysis is carried out to verify the operation and efficiency of the proposed PD technique. In general, the obtained results demonstrate linearization and I/Q modulator calibration performance clearly exceeding the performance of current state-of-the-art reference techniques.