They offer faster access to help but less time with a therapist, which may not suit everyone, the health body recommending them said.
There is huge demand for face-to-face services, with people waiting several weeks to see a therapist.
Psychiatrists said digital therapies were not a long-term solution.
Mental-health charity Sane said they were no substitute for a one-to-one relationship and could leave people feeling even more isolated than before.
One out of every six people in England says they experience a common mental-health problem such as anxiety and depression in any given week.
In 2021-22, more than half a million people were referred to depression and anxiety services - called NHS Talking Therapies - for problems such as body-dysmorphic disorder, panic disorder, post-traumatic stress disorder (PTSD), obsessive-compulsive disorder and a variety of phobias.
The new digital therapies, delivered via a website or an app using cognitive-behavioural therapy (CBT), provide an alternative way of accessing support, which may be more convenient for some, the National Institute for Health and Care Excellence (NICE) says.
They could also free up resources and help reduce the wait for care.
Its guidance recommends six therapies designed to treat adults with anxiety disorders and three to treat those with depression, including Beating the Blues, Deprexis and Space from Anxiety.
Before treatment starts, there is a formal assessment with a trained clinician or practitioner but after that, clinicians are involved much less:
* During online depression therapy, 90 minutes is spent with a therapist instead of eight hours during standard care
* Online anxiety therapy gives four hours with a clinician, as opposed to 10 hours under normal care
Dr David Rigby, who jointly chairs the Royal College of Psychiatrists' digital group, said digital therapies could make it easier for some vulnerable patients to access vital mental-health support but were not a long-term solution.
"Mental health services are struggling with chronic staff shortages which are making it difficult for them to provide patients with quick and effective treatment," he said.
"The government must tackle the workforce crisis by honouring its commitment to publish a comprehensive NHS workforce plan this year."
Sane founder and chief executive Marjorie Wallace CBE digital therapy "may be very useful for some" but was "no substitute for a one-to-one relationship with someone who knows their story".
"Our experience with those who contact us is that self-diagnosis and techniques of self-management do not always reach the layers of their inner mental pain and can leave them feeling even more unsafe and alone," she said.
NICE interim director of medical technology and digital evaluation Mark Chapman said: "One of our priorities is to get the best care to people fast while at the same time ensuring value for money for the taxpayer - these digitally enabled therapies do both." But the choice of online therapy "must be the right one for the individual".
While some of the digital therapies are already in use, others require further approvals being they can be rolled out.
NICE will look at the evidence from their use over the next few years to work out how cost-effective they are.