Gate-tunable Josephson junctions (JJs) are the backbone of superconducting classical and quantum computation. Typically, these systems exploit low charge concentration materials, and present technological difficulties limiting their scalability. Surprisingly, electric field modulation of supercurrent in metallic wires and JJs has been recently demonstrated. Here, we report the realization of titanium-based monolithic interferometers which allow tuning both JJs independently via voltage bias applied to capacitively-coupled electrodes. Our experiments demonstrate full control of the amplitude of the switching current (IS) and of the superconducting phase across the single JJ in a wide range of temperatures. Astoundingly, by gate-biasing a single junction the maximum achievable total IS suppresses down to values much lower than the critical current of a single JJ. A theoretical model including gate-induced phase fluctuations on a single junction accounts for our experimental findings. This class of quantum interferometers could represent a breakthrough for several applications such as digital electronics, quantum computing, sensitive magnetometry and single-photon detection.The possibility of tuning the properties of Bardeen-Cooper-Schrieffer (BCS) metallic superconductors via conventional gating has been excluded for almost a century. Surprisingly, strong static electric fields have been recently shown to modulate the supercurrent down to full suppression and even to induce a superconductorto-normal phase transition in metallic wires [1,2] and Josephson junctions (JJs) [3-5] without affecting their normal-state behavior. Yet, these results did not find a microscopic theoretical explanation so far [6]. In this Article, we lay down a fundamental brick for both the insight and the technological application of this unorthodox field-effect by realizing a titanium-based monolithic superconducting quantum interference device (SQUID) which can be tuned by applying a gate bias to both JJs independently. We first show modulation of the amplitude and the position of the interference pattern of the switching current (I S ) by acting with an external electric field on a single junction of the interferometer. Notably, this phenomenology differs from that of conventional gatetunable SQUIDs [7-10] and cannot be explained by a simple squeezing of the critical current of the junction induced by the electric field [11]. Consequently, a local electric field acts on a global scale influencing the properties of both JJs. Since the superconducting phases of the two JJs are non-locally connected by fluxoid quantization, we deduce that the electric field must act both on the critical current amplitude and couple to the superconducting phase across the single junction. The overall interferometer phase can shift from −0.4π to 0.2π depending on the used gate electrode and on the strength of the gate bias. Furthermore, the effect persists up to ∼ 80% of the superconducting critical temperature.Fully-metallic field-effect controllable Josephson...