Chaos synchronization by external common noise is an intriguing phenomenon in chaotic dynamical systems in connection with application to secure communication and generalized synchronization. When common arbitrary noise is added to identical chaotic systems externally, the systems are synchronized at a certain region of the noise amplitude. In apart from these studies, phase synchronization is also extensively studied. When two slightly different chaotic systems are coupled with each other, their phases begin to be synchronized when the coupling strength exceeds the critical value. Here, we study phase synchronization in diode lasers by applying a common noise-like signal simultaneously. In the experiment, when two diode lasers generate chaotic outputs, we feed a common noise-like signal to the laser drivers simultaneously. Then, each laser pumped by dc current is modulated by the noise-like signal. We observe the transition to phase synchronization as the amplitude of the noise-like signal increases. When the amplitude exceeds a critical voltage, the phases of the two lasers are synchronized with a time delay. Before phase synchronization, the dynamics shows intermittent phase jumps, which is similar to that appearing in coupled chaotic oscillators. This transition due to the common noise-like signal is a new phenomenon that has not been reported yet. We study the characteristics of the transition to phase synchronization in the phase spaces. And phase synchronization and intermittent phase jumps are analyzed by the dynamics of the phase difference of the two lasers according to the amplitude of the noise-like signal.