Concerns for her welfare were raised by Paul Netherton, assistant chief constable at Devon and Cornwall Police.
He spoke out on Twitter on behalf of the girl, who had been held in a cell since Thursday because, he said, no beds were available anywhere in the UK.
NHS England said the 16-year-old would be moved on Saturday night.
A spokesman said: "After details were provided to NHS England about the girl and her condition, a place was found locally within a few hours.
"We are grateful for the help of the NHS in the area in identifying the place.
"It is worth noting that mental health crisis services have been expanding so that the number of people ending up in police cells is in fact down - but clearly more needs to be done."
Earlier on Twitter, Mr Netherton had described the situation as "unacceptable".
He tweeted: "We have a 16yr old girl suffering from mental health issues held in police custody. There are no beds available in the uk!
"The 16yr old was detained on Thursday night, sectioned Friday lunchtime and still no place of safety available. This can't be right!
"Custody on a Fri & Sat night is no place for a child suffering mental health issues. Nurses being sourced to look after her in custody !?!"
He later  tweeted: "Just heard that a place of care has been found for our 16yr old. Good result."
Mr Netherton told BBC News the girl had been arrested at Torbay Hospital on Thursday after a breach of the peace and sectioned under the Mental Health Act on Friday because she was "obviously very unwell".
"We shouldn't have children, a schoolgirl, staying overnight in a custody block," he said.
According to the officer, 750 mental health patients had been placed in police cells across Devon and Cornwall so far this year.
Shadow health minister Luciana Berger described the teenager's predicament as "an appalling reflection of the crisis in mental health services".
"People shouldn't face the indignity of being kept in police cells when they are at their most vulnerable," she said.
Mark Winstanley, chief executive of mental health charity Rethink, said: "Each year thousands of people with serious mental health problems are being held in police cells, including many children and teenagers, because the right services either don't exist in their community or are completely overstretched.
"Many people are being turned away from places of safety, because of staff shortages or lack of spaces.
"In some parts of the country, there are no health-based places of safety full-stop.
"As a result, people end up being held in police stations, or are simply left to fend for themselves. This has to change, as it's costing lives.
"Someone going through a physical health emergency would never be treated this way, so why should it be acceptable for people experiencing a mental health crisis?"
A teenage girl with mental health problems who was kept in police cells for two days because of a lack of care beds has been found a place to stay.