Back in 1987, a small study measured the effect of autogenic training on tension headaches. They found about autogenic training is effective in reducing tension headaches. It is well-established relaxation techniques such as AT, meditation, progressive muscle relaxation help with tension headaches.
This is not unexpected since stress often causes tension headaches. But everyone is not the same, some may get more relief from pain than others and it is impossible to predict that. Nevertheless, practicing relaxation is beneficial for many reasons. You may have anxiety if you have tension headaches and relaxing regularly often helps with feelings of anxiety. That is even more so if you have a lot of stress during your normal days. Practicing autogenic training or meditation surely makes you feel calm and that improves the quality of life.
Relaxation also increases melatonin and serotonin. Melatonin is a sleep hormone and naturally induces sleep. My clients with autogenic training ALL report better sleep. They fall asleep sooner and after the course, almost all need an alarm clock if they did not need it earlier. Serotonin is connected with depression. Autogenic training is proved to help feelings of depression and that does not come as a surprise, since everybody feels better after you do a relaxation technique.
Tension headaches are a real problem for many and everybody has these headaches here and there. If you practice autogenic training regularly, your average stress levels drop significantly. That can be a huge help with tension headaches if not a complete absence of them.