An attachment system for attaching panels to a wall, wherein at least one of said panels has a front surface, a back surface, an upper edge and a lower edge, and is provided with multiple pairs of mutually parallel grooves through the back surface of the panel, which attachment system comprises: - at least two support profiles configured to be fixed vertically to the wall and shaped so that an L-shaped section (4,5) of the support profiles, extends outward from the wall when the profiles are fixed thereto, said section comprising a first leg portion and a second leg portion, with the first leg portion oriented transversely with respect to the wall and the second leg portion at a distance from the wall and essentially parallel thereto, - a plurality of support brackets configured for fixation into the grooves, each support bracket comprising an assembly of a first and a second bracket profile (15, 16), each including a leg portion for fixation into a groove and a wall portion extending away from the leg portion and, after assembly, from the panel, characterised in that each pair of grooves are configured to be oriented in the vertical direction when the panel is mounted to the wall, and in that the first and second bracket profiles (15,16) each comprise at least one transversal portion (24;25,26,32) at the top of the respective wall portions, the transversal portions being shaped so as to form a half-closed space when the bracket is assembled, into which half closed space the second leg portion of the L-section of a support profile can be slidably inserted, thereby enabling the panel provided with multiple assembled brackets to be moved horizontally relative to the support profiles until the second leg portion of the L-section of at least two support profiles slides into the half-closed spaces of a plurality of brackets. - at least two support profiles configured to be fixed vertically to the wall and shaped so that an L-shaped section (4,5) of the support profiles, extends outward from the wall when the profiles are fixed thereto, said section comprising a first leg portion and a second leg portion, with the first leg portion oriented transversely with respect to the wall and the second leg portion at a distance from the wall and essentially parallel thereto, - a plurality of support brackets configured for fixation into the grooves, each support bracket comprising an assembly of a first and a second bracket profile (15, 16), each including a leg portion for fixation into a groove and a wall portion extending away from the leg portion and, after assembly, from the panel, characterised in that each pair of grooves are configured to be oriented in the vertical direction when the panel is mounted to the wall, and in that the first and second bracket profiles (15,16) each comprise at least one transversal portion (24;25,26,32) at the top of the respective wall portions, the transversal portions being shaped so as to form a half-closed space when the bracket is assembled, into which half closed space the second leg portion of the L-section of a support profile can be slidably inserted, thereby enabling the panel provided with multiple assembled brackets to be moved horizontally relative to the support profiles until the second leg portion of the L-section of at least two support profiles slides into the half-closed spaces of a plurality of brackets.