According to the Harvard Mental Health Letter, the answer is yes. There are a number of solid studies which suggest that yoga modulates our stress responses. You can read the full article via the link at the end of this post and get details of the research trials conducted and how these results. The main findings, however, are posted below:
Yoga modulates the stress response by reducing perceived stress and anxiety. This, in turn, decreases physiological arousal — for example, reducing the heart rate, lowering blood pressure, and easing respiration. There is also evidence that yoga practices help increase heart rate variability, an indicator of the body’s ability to respond to stress more flexibly.
Improved mood and functioning
Questions remain about exactly how yoga works to improve mood, but preliminary evidence suggests its benefit is similar to that of exercise and relaxation techniques.
In a German study published in 2005, 24 women who described themselves as “emotionally distressed” took two 90-minute yoga classes a week for three months. Women in a control group maintained their normal activities and were asked not to begin an exercise or stress-reduction program during the study period.
Though not formally diagnosed with depression, all participants had experienced emotional distress for at least half of the previous 90 days. They were also one standard deviation above the population norm in scores for perceived stress (measured by the Cohen Perceived Stress Scale), anxiety (measured using the Spielberger State-Trait Anxiety Inventory), and depression (scored with the Profile of Mood States and the Center for Epidemiological Studies Depression Scale, or CES-D).
At the end of a three month trial, women who described themselves as “emotionally distressed” (although not formally diagnosed with depression) reported improvements in perceived stress, depression, anxiety, energy, fatigue, and well-being after taking two 90 minute yoga classes per week. Depression scores improved by 50%, anxiety scores by 30%, and overall well-being scores by 65%. Initial complaints of headaches, back pain, and poor sleep quality also resolved much more often in the yoga group than in the control group.
Further controlled trials of yoga practice have demonstrated improvements in mood and quality of life for the elderly, people caring for patients with dementia, breast cancer survivors, and patients with epilepsy.
Benefits of controlled breathing
A type of controlled breathing with roots in traditional yoga shows promise in providing relief for depression. The program, called Sudarshan Kriya yoga (SKY), involves several types of cyclical breathing patterns, ranging from slow and calming to rapid and stimulating. One study even suggests that SKY might be a beneficial treatment for depression in the early stages of recovery from alcoholism.
Potential help for PTSD
Since evidence suggests that yoga can tone down maladaptive nervous system arousal, researchers are exploring whether or not yoga can be a helpful practice for patients with post-traumatic stress disorder (PTSD).
One randomized controlled study examined the effects of yoga and a breathing program in disabled Australian Vietnam veterans diagnosed with severe PTSD. The veterans were heavy daily drinkers, and all were taking at least one antidepressant. Six weeks after the study began, the yoga and breathing group showed improvements which persisted at a six-month follow-up. The control group, consisting of veterans on a waiting list, showed no improvement.
Researchers at the Walter Reed Army Medical Center in Washington, D.C., are offering a yogic method of deep relaxation to veterans returning from combat in Iraq and Afghanistan. Dr. Kristie Gore, a psychologist at Walter Reed, says the military hopes that yoga-based treatments will be more acceptable to the soldiers and less stigmatizing than traditional psychotherapy. The center now uses yoga and yogic relaxation in post-deployment PTSD awareness courses, and plans to conduct a controlled trial of their effectiveness in the future.

Note:
Although many forms of yoga practice are safe, some are strenuous and may not be appropriate for everyone. In particular, elderly patients or those with mobility problems may want to check first with a clinician before choosing yoga as a treatment option.
But for many patients dealing with depression, anxiety, or stress, yoga may be a very appealing way to better manage symptoms. Indeed, the scientific study of yoga demonstrates that mental and physical health are not just closely allied, but are essentially equivalent. The evidence is growing that yoga practice is a relatively low-risk, high-yield approach to improving overall health.

For more information and access to the data of these studies, see http://www.health.harvard.edu/mind-and-mood/yoga-for-anxiety-and-depression