The government said hopes schools and other bodies will use the "state of the nation" report to inform their policies and management of children's mental health from October 2019.
The document will highlight trends and issues in young people's mental health based on existing data collected by the Office for National Statistics, such as student satisfaction levels, alongside data on children's physical health and academic attainment.
The Department for Education will also provide new guidance to teachers next year to help them measure students' health, including their mental wellbeing.
The tool is intended to be used voluntarily by schools, and will not include any formal assessment of students or require teachers to report back to government. The government hopes it will help education professionals spot signs of poor mental health, and enable them to build on existing supportive measures.
It will operate alongside plans for health and mental health to be included in school curriculums for all state-funded schools from 2020 - proposals that are currently the subject of a government consultation on relationships and sex education.
Theresa May said the plans would go towards giving children's mental wellbeing "the priority it so profoundly deserves".
"I have made parity of care a priority for our long-term plan for the NHS," she said.
"As a result, our record investment in the NHS will mean record investment in mental health.
"We need true parity between physical and mental health - and not just in our health systems - but in our classrooms, workplaces and communities too."
Alongside the announcements, May said recruitment has begun for mental health support teams of trained individuals who will provide interventions and provide support to groups of primary and secondary schools, as detailed in the government's December 2017 green paper Transforming Children and Young People's Mental Health.
Trainees are set to begin studying in January, and join schools across England next year. May has also appointed Jackie Doyle-Price as a new minister for suicide prevention.
YoungMinds director of policy Marc Bush said while there were still "big questions" left unanswered by government about future funding for NHS children's mental health services, the announcements were positive for schools.
"The wellbeing of children should be every bit as important as academic performance, and schools need the tools and resources to make this a priority" said Bush.
"Mental health support teams could make a real difference, though the programme needs to be expanded so that it reaches all schools and students.
"New state of the nation reports and student wellbeing measures will help to provide robust evidence about which mental health initiatives are most effective.
"Only by having up-to-date insights about the experience of young people can we hope to address the current crisis."
Max Davie, officer for health promotion at the Royal College of Paediatrics and Child Health, said he hoped the State of the Nation report would be used to identify areas of need for children and adolescent mental health services and other interventions.
"Half of all mental health problems are already established by the age of 14, so focusing on prevention and early intervention is vital," he said.
"However, more needs to be done for those children who already have mental and emotional health needs.
"These children and young people should have timely and appropriate access to evidence-based services and treatment, with these services considered an integral part of children's healthcare in both acute and community settings."
Place2Be chief executive Catherine Roche agreed the report would help bring transparency to the scale of mental health problems faced by young people.
"The state of the nation report proposed by the Prime Minister could be a hugely helpful step forward in monitoring progress to ensure that children and young people are getting the support that they need," she said.
"Schools have a vital role to play in promoting positive mental health and building children's resilience to cope with life's inevitable challenges, and new tools to help schools measure student health and wellbeing will be gratefully received.
"It will be important that they are backed up by professional support where problems are identified."