The proper characterization of the turbulence structure in an astronomical site requires a statistical analysis of the refractive index structure constant, CN2(h). Our team has been monitoring this variable since November 2002 at the Teide Observatory (Tenerife, Canary Islands, Spain). We have derived the seasonal evolution of turbulence structure at this site using data from more than 150 nights of useful G-SCIDAR measurements. The monthly statistical profiles for different years present a similar structure for different years, suggesting a stable seasonal evolution of the turbulence at the Canary Islands sites. From this statistical analysis, we have derived the seasonal evolution of the Fried's parameter, the isoplanatic angle and the coherence time. The average values for these parameters are < r0 >=15.1+/-4.6 cm, <θ0 >= 2.7+/-1.3 arcsec and <τ0 >= 5.8 +/- 3.1 ms. Uncertainties indicate the standard deviation of the averaged measurements. These statistical values for atmospheric adaptive optics parameters and their smooth seasonal behavior bring up the sky quality of the Canary Islands astronomical sites for the implementation of adaptive optics systems.