Assembly system of tubular element furniture, with tubular elements (1,1') and connecting elements (2,2') to connecting nodes (3) along the three directions of space (X,Y,Z). The connecting nodes (3) have a vertical tubular body (4) with a frustoconical interior void (5). The connecting elements (2) of the horizontal tubular elements (1) have a frustoconical sector (7) of a quarter of the interior void (5) of the connecting nodes (3), and are introduced into the interior void (5) of the connecting nodes (3) filling said interior void (5) leaving an vertical internal through-hole (10), and the connecting elements (2') of the vertical tubular elements (1) have configured tongue and groove means traversing the vertical internal through-hole (10) of the connecting nodes (3) carrying out closure and fixing of the tubular elements (1,1') to the connecting node (3).