We study the magnetization damping in ion-beam deposited Co72Fe18B10 thin films as a function of film thickness and crystalline state. As-deposited amorphous layers showed low damping (αapp=0.006) that is thickness independent. 40nm Co80Fe20 with no boron content exhibited a value twice higher (αapp=0.013). Crystallization in Co72Fe18B10, triggered by annealing at 280°C, results in increased magnetization as well as a strong increase in damping, by a factor of 5 for 40nm films. For lower thicknesses the damping increase upon annealing is less pronounced. The exchange stiffness constant for amorphous films is deduced from perpendicular standing spin waves to be 28.4×10−12J∕m. The annealing dependence of damping should have consequences for the spin-transfer switching in CoFeB∕MgO∕CoFeB magnetic tunnel junctions.