The pair came first and second in the final round of internal voting for the Conservative leadership contest, while Michael Gove was eliminated.
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Following the bruising European Union referendum campaign and the resignation of David Cameron, the Home Secretary has insisted she can unite the party.
While Mrs May enjoys a clear advantage among Tories at Westminster, she will be acutely aware that Mrs Leadsom could attract votes from Eurosceptic activists who want a “Brexit prime minister” to oversee withdrawal negotiations.
Britain’s first female prime minister was Margaret Thatcher, a Conservative who governed from 1979 to 1990.
The victor will replace Prime Minister David Cameron, who resigned after Britain decided last month in a referendum to leave the European Union in a vote dubbed “Brexit”.
The pro-Brexit Ms Leadsom has attracted support from a series of leading figures in Ukip since announcing her candidacy, including the party’s major donor Arron Banks. She has never held a Cabinet position before, but is staunchly in favor of Brexit-something that could draw party support.
She campaigned to remain in the EU but has said she is committed to ensuring the best deal for UK’s exit from the union.
Gove said that he was “naturally disappointed” by the result.
Former Tory leader Iain Duncan Smith, who is backing Mrs Leadsom, said she had “real steel” but within the “velvet glove of compassion”.
Whomever wins the battle of the fierce women will then become a replacement for David Cameron in Number 10, by September 9. The betrayal probably hurt his leadership chances, fueling a view among Tories that he is disloyal.
She said Mrs May, who was state educated, wanted to ensure that “government is for everyone in this country” and not just “those privileged few”.
May, Britain’s interior minister for the past six years, is the runaway favourite among lawmakers but the Conservatives have a history of not choosing the favourite.
Earlier in the day, Mrs Leadsom pitched herself as the “prosperity not austerity” candidate.
She also won the support of Education Secretary Nicky Morgan, who had previously backed Michael Gove, and the leader of the Scottish Conservatives, Ruth Davidson.
“Now is the time for me and my team to take my case out to the party members in the country”, she told the press outside Parliament shortly after the result was declared.
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Leadsom, a relative political novice who entered parliament in 2010, campaigned for the Leave campaign. She denies the claims.
