A heat exchanger (1) for gas condensing boilers is provided with a container body (2) within which at least one pipe bundle (3) is disposed to delimit a combustion chamber (300). The at least one pipe bundle (3) is made by a pipe spiral wound around a central axis. A first end (31) of the pipe serves as an inlet for the heat transfer fluid to be heated. A second end (32) of the pipe serves as an outlet for said heat transfer fluid. The pipe bundle (3) is made as a single component defined by a seamless single element. The pipe bundle has an elliptical section with said ends (31; 32) having a circular section projecting from said container body (2), so as to be accessible from the outside, to ease the operations of connection of the ends (31; 32) to the pipes of the water system. A method of manufacturing the pipe bundle (3) involves shaping an elliptical section of a pipe by mechanical processes for plastic deformation, so as to obtain a change of section, from elliptical to circular, thus allowing a metallic continuity between the exchanger and the pipes of the water system.