Thermal treatment of carbon nanotubes (CNTs) can significantly improve their mechanical, electrical and thermal properties due to reduced defects and increased crystallinity. In this work we investigate the effect of annealing at 3000 °C of vertically aligned CNT arrays synthesized by chemical vapor deposition (CVD) on graphite. Raman measurements show a drastically reduced amount of defects and, together with transmission electron microscope (TEM) diffraction measurements, an increased average crystallite size of around 50%, which corresponds to a 124% increase in Young's modulus. We also find a tendency for CNTs to bond to each other with van der Waals (vdW) forces, which causes individual CNTs to closely align with each other. This bonding causes a densification effect on the entire CNT array, which appears at temperatures >1000 °C. The densification onset temperature corresponds to the thermal decomposition of oxygen containing functional groups, which otherwise prevents close enough contact for vdW bonding. Finally, the remaining CVD catalyst on the bottom of the CNT array is evaporated during annealing, enabling direct anchoring of the CNTs to the underlying graphite substrate.