Net long-term migration to the UK was 333,000 in 2015 - the second highest level on record, official figures show.
According to the Office for National Statistics this is up 20,000 on the figure for 2014.
The statistics show the number of EU citizens moving to the UK in 2015 was 184,000- up 10,000 on the previous year.
Boris Johnson said the figures showed the "failure" of David Cameron to control migration as promised.
The Conservative Party had pledged to keep immigration to the "tens of thousands".
The former London mayor, who is a leading Brexit campaigner, said he was "in favour" of immigration and the benefits it brought.
But he claimed there should be a clamdown on "uncontrolled immigration" and called for Britain to "take back control of its borders".
"Britain benefits from cultural influences from abroad. I'm pro-immigration, but above all I'm pro-controlled immigration.
"People of all races and backgrounds in the UN are genuinely concerned about uncontrolled immigration and the pressure it's placing on local services.
"People have every right to question why we can't control our borders. We need to answer those concerns by taking back control of those borders"
He added that freedom of movement rules meant the government was "unfairly" excluding engineers and doctors from countries such as India and Australia because it had "no control" over EU immigration.
Fellow Brexiteer Nigel Farage joined Johnson in condemnation of the figures released today, commenting that they showed "mass immigration is still hopelessly out of control and set to get worse if we Remain inside the EU, going on with disastrous open borders".
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