Anomaly mediation models are well motivated supersymmetry breaking scenarios which appear as alternatives to the mSUGRA paradigm. These models are quite compelling from the theoretical point of view and it is therefore important to test if they are also viable models for phenomenology. We perform a study of these models in the light of all standard flavour, collider and dark matter constraints, including also the recent Higgs boson measurements for the mass and signal strengths in the different decay channels. The minimal AMSB scenario can satisfy in part of its parameter space the dark matter requirement but is only marginally consistent with the current Higgs boson mass value. The HyperCharge-AMSB and Mixed Moduli-AMSB scenarios can better describe present data from dark matter, flavour, low energy physics and are consistent with the measured mass of the Higgs boson. The inclusion of the preferred signal strengths for the Higgs boson decay channels shows that for tan(beta) > 5 the HC-AMSB and MM-AMSB models can be consistent with the present Higgs boson data. In contrast the minimal AMSB has a narrower allowed range in tan(beta). These different AMSB scenarios, while consistent with present Higgs boson measurements, can be further tested by future more precise data in the Higgs sector.