There are clinical studies which have established the effectiveness of online therapy. You can find a small selection of these studies below:
“Internet-based versus face-to-face cognitive-behavioral intervention for depression: A randomized controlled non-inferiority trial”
Andersson, G., & Cuijpers, P. “Internet-based and other computerized psychological treatments for adult depression: A meta-analysis.” Cognitive Behaviour Therapy, 38(4), 196-205.
Barak, Azy, et al. “A comprehensive review and a meta-analysis of the effectiveness of internet-based psychotherapeutic interventions.” Journal of Technology in Human Services, 26.2-4: 109-160.
Wantland, D. J., Portillo, C. J., Holzemer, W. L., Slaughter, R., & McGhee, E. M. (2004). “The effectiveness of Web-based vs. non-Web-based interventions: a meta-analysis of behavioral change outcomes.” Journal of Medical Internet Research, 6(4).
“Home telemental health implementation and outcomes using electronic messaging.”