Jeremy Hunt, who had widely been expected to throw his hat into the ring, gave his backing to May instead
That followed announcements by Michael Gove and Andrea Leadsom this morning. Liam Fox and Stephen Crabb have also said they will run, while Boris Johnson is expected to make an announcement later today.
In her announcement today, May said there will be no early General Election, and that she will not trigger Article 50, which allows the UK to leave the EU, until an exit strategy is clear.
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"Whether you supported Leave or Remain in the referendum campaign, and whether you predicted the sky would fall in or you didn't, the result means we face a period of uncertainty that needs to be addressed head-on," she said this morning.
"The country needs strong leadership and a clear sense of direction to give a confidence to investors, to keep the economy moving and to keep people in work."
She added that under her leadership there will be no second EU referendum, saying "Brexit means Brexit".
"The campaign was fought, the vote was held, turnout was high and the public gave their verdict."
Commons leader Chris Grayling offered his backing to May, saying: "I want a Prime Minister who's been there, who's done it, who's debated difficult challenges for the UK - and that is Theresa".