Mrs Leadsom said Theresa May was ideally placed to implement Brexit and offered the Home Secretary her full support.
News of Mrs Leadsom’s planned statement came moments after Mrs May launched her national campaign with a speech in Birmingham in which she presented herself as the candidate of unity and experience, with the backing of an “overwhelming” majority of Tory MPs at Westminster.
The Home Secretary took top slot in the MPs’ ballot last week with 199 votes to her rival’s 84.
Mrs Leadsom’s campaign got off to a disastrous start after she was forced to apologise to Mrs May for a newspaper interview in which she appeared to suggest that being a mother gave her an edge over the childless Home Secretary as a future prime minister.
In a televised statement Mrs Leadsom said: “The best interests of our country inspired me to stand for the leadership.
“I believe that in leaving the EU a bright future awaits, where all our people can share in a new prosperity, freedom and democracy.
“The referendum result demonstrated a clear desire for change - strong leadership is needed urgently to begin the work of withdrawing from the European Union.
“A nine-week leadership campaign at such a critical moment for our country is highly undesirable.
The energy minister - who entered Parliament in 2010 and has never held a Cabinet post - admitted that she had been “shattered” by the experience of intensive media scrutiny, which also involved questions about apparent inaccuracies on her CV and demands for her to publish her tax returns.
Former London mayor Boris Johnson - who abandoned an expected tilt for the leader’s job after realising he faced competition from both Mrs Leadsom and Mr Gove - said he had “no doubt” that Mrs May would make an excellent party leader and PM.
Mr Johnson said: “Theresa May will provide the authority and the leadership necessary to unite the Conservative Party and take the country forward in the coming weeks and months.
“Andrea’s decision, which is both brave and principled, allows that process to begin immediately.
“I have no doubt Theresa will make an excellent party leader and Prime Minister and I’m encouraged that she’s made it clear that Brexit means Brexit - that we will leave the EU.
“It is vital that we respect the will of the people and get on with exploiting new opportunities for this country.”
Mrs May left the venue of her campaign launch speech in Birmingham before reporters there were able to ask her about Mrs Leadsom’s statement.