The ability to manipulate the spectral-temporal waveform of optical pulses in the classical domain has enabled a wide range of applications from ultrafast spectroscopy to high-speed communications. Extending these concepts to quantum light has the potential to enable breakthroughs in optical quantum science and technology. However, filtering and amplifying often employed in classical pulse shaping techniques are incompatible with non-classical light. Controlling and efficiently measuring the pulsed mode structure of quantum light requires efficient means to achieve deterministic, unitary manipulation that preserves fragile quantum coherences. Here an approach to deterministically modify the pulse-mode structure of quantum states of light within an integrated optical platform is presented. The method is based upon application of both spectral and temporal phase modulation to the wave packet. These techniques lay the ground for future quantum wavelength- and time-division multiplexing applications and facilitate interfacing of different physical platforms where quantum information can be stored and manipulated.