A direct observation of Anderson localization of matter-waves in a controlled disorder is reported. The study observes exponential localization of a Bose-Einstein condensate (BEC) in a one-dimensional waveguide with a controlled disorder created by laser speckle. The experiment operates in a regime allowing Anderson localization (AL): weak disorder and negligible atomic interactions. Direct imaging of the atomic density profiles shows that weak disorder leads to the stopping of expansion and the formation of a stationary exponentially localized wave function, a direct signature of AL. The localization length is extracted by fitting the exponential wings of the density profiles and compared to theoretical calculations. The results show that exponential localization occurs only when the de Broglie wavelengths of the atoms are larger than an effective mobility edge corresponding to the spatial frequency cut-off of the disorder. In the opposite case, the density profiles decay algebraically. The method can be extended to higher dimensions and with controlled interactions. The experiment demonstrates the high degree of control in the setup and its potential for investigating Anderson localization in higher dimensions. The results support the existence of a cross-over from exponential to algebraic regimes in a 1D speckle potential. The study highlights the importance of direct imaging of atomic quantum gases in controlled optical disordered potentials for investigating disordered quantum systems. The findings have implications for understanding Anderson localization in various quantum systems, including Bose and Fermi gases, and for developing quantum simulators.A direct observation of Anderson localization of matter-waves in a controlled disorder is reported. The study observes exponential localization of a Bose-Einstein condensate (BEC) in a one-dimensional waveguide with a controlled disorder created by laser speckle. The experiment operates in a regime allowing Anderson localization (AL): weak disorder and negligible atomic interactions. Direct imaging of the atomic density profiles shows that weak disorder leads to the stopping of expansion and the formation of a stationary exponentially localized wave function, a direct signature of AL. The localization length is extracted by fitting the exponential wings of the density profiles and compared to theoretical calculations. The results show that exponential localization occurs only when the de Broglie wavelengths of the atoms are larger than an effective mobility edge corresponding to the spatial frequency cut-off of the disorder. In the opposite case, the density profiles decay algebraically. The method can be extended to higher dimensions and with controlled interactions. The experiment demonstrates the high degree of control in the setup and its potential for investigating Anderson localization in higher dimensions. The results support the existence of a cross-over from exponential to algebraic regimes in a 1D speckle potential. The study highlights the importance of direct imaging of atomic quantum gases in controlled optical disordered potentials for investigating disordered quantum systems. The findings have implications for understanding Anderson localization in various quantum systems, including Bose and Fermi gases, and for developing quantum simulators.