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Priti Patel has resigned as UK international development secretary amid controversy over her meetings with Israeli officials.
She was ordered back from an official trip in Africa by the PM and summoned to Downing Street over the row.
In her resignation, Ms Patel apologised and said her actions "fell below the standards of transparency and openness that I have promoted and advocated".
The PM said her decision was "right" as "further details have come to light".
Ms Patel had apologised to Mrs May on Monday after unauthorised meetings with Israeli politicians in August came to light, but it later emerged she had two further meetings without government officials present in September.
Ms Patel had a 30 minute meeting with Mrs May, arriving at 10 Downing Street via the back door after returning to the UK.
Her resignation from the cabinet is the second in seven days, after Sir Michael Fallon quit as defence secretary on Wednesday last week amid allegations about his behaviour.
In her letter to Theresa May, Ms Patel said: "While my actions were meant with the best of intentions, my actions also fell below the standards of transparency and openness that I have promoted and advocated.
"I offer a fulsome apology to you and to the government for what has happened and offer my resignation."
Image caption Priti Patel's resignation letter In her reply, Mrs May said: "Now that further details have come to light, it is right that you have decided to resign and adhere to the high standards of transparency and openness that you have advocated."
She added that Ms Patel should "take pride" in what had been achieved during her time as secretary of state.
The BBC's chief political correspondent Vicki Young said Theresa May "decided to give her colleague the dignity of resigning".
But she said the response from Mrs May was "interesting", saying: "It was clear from Theresa May that if she hadn't resigned, she would have been sacked."
She was ordered back from an official trip in Africa by the PM and summoned to Downing Street over the row.
In her resignation, Ms Patel apologised and said her actions "fell below the standards of transparency and openness that I have promoted and advocated".
The PM said her decision was "right" as "further details have come to light".
Ms Patel had apologised to Mrs May on Monday after unauthorised meetings with Israeli politicians in August came to light, but it later emerged she had two further meetings without government officials present in September.
Ms Patel had a 30 minute meeting with Mrs May, arriving at 10 Downing Street via the back door after returning to the UK.
Her resignation from the cabinet is the second in seven days, after Sir Michael Fallon quit as defence secretary on Wednesday last week amid allegations about his behaviour.
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In her letter to Theresa May, Ms Patel said: "While my actions were meant with the best of intentions, my actions also fell below the standards of transparency and openness that I have promoted and advocated.
"I offer a fulsome apology to you and to the government for what has happened and offer my resignation."
Image caption Priti Patel's resignation letter In her reply, Mrs May said: "Now that further details have come to light, it is right that you have decided to resign and adhere to the high standards of transparency and openness that you have advocated."
She added that Ms Patel should "take pride" in what had been achieved during her time as secretary of state.
The BBC's chief political correspondent Vicki Young said Theresa May "decided to give her colleague the dignity of resigning".
But she said the response from Mrs May was "interesting", saying: "It was clear from Theresa May that if she hadn't resigned, she would have been sacked."