Miniaturized, ultra-sensitive and easily integrable magnetometers are needed for many applications like space exploration or medical survey. In this study, we combine innovative magnetic tunnel junctions having a symmetric resistance-field (R–H) response with a high gain flux concentrator. In our junctions, the magnetization of the free layer (FL) is stabilized in an anti-parallel configuration with respect to that of the reference layer. This configuration is achieved by using a soft exchange pinning of the FL. We precisely adjust the exchange field value with a dusting layer of ruthenium used to weakly decouple the magnetization of the FL from the local moments of the antiferromagnet. In order to improve the junction's sensitivity, we study the influence of the exchange field value and of the shape anisotropy on the even-function R–H response. In particular, we compare circular junctions with elliptic or rectangular junctions of various aspect ratios and orientations. We find that the sensitivity of the junctions increases when reducing the soft-pinning exchange field and by using junctions with an elongated shape in the direction of the applied field. Finally, we were able to further increase the sensitivity by a factor 440 due to a flux concentrator placed around the junction by electrochemical deposition of NiFe. Its design is optimized (elongated shape, 5–7 μm thickness and 10 μm air-gap) in order to obtain this very high gain. The complete sensor system composed of these magnetic tunnel junctions and the flux concentrator allows to reach sensitivities larger than 1000%/mT.