The speckle pattern produced when a laser is scattered by a disordered medium has recently been shown to give a surprisingly accurate or broadband measurement of wavelength. Here it is shown that deep learning is an ideal approach to analyze wavelength variations using a speckle wavemeter due to its ability to identify trends and overcome low signal to noise ratio in complex datasets. This combination enables wavelength measurement at high precision over a broad operating range in a single step, with a remarkable capability to reject instrumental and environmental noise, which has not been possible with previous approaches. It is demonstrated that the noise rejection capabilities of deep learning provide attometre‐scale wavelength precision over an operating range from 488�nm to 976�nm. This dynamic range is six orders of magnitude beyond the state of the�art.