Israel said in September it would shut the British consulate, in retaliation for UK sanctions on Israeli settlements in the occupied West Bank which are illegal under international law.
The UK government had made last-ditch efforts to persuade Israel not to close the building ahead of Thursday's deadline, after the Israeli government said it would close the consulate within 30 days of the UK sanctions announcement.
Most diplomats will leave the British consulate in occupied East Jerusalem, Israel says, but the UK insists the building "will not be closing", and will operate as a "UK Mission".
The BBC's Middle East correspondent Yolande Knell says the UK Foreign Secretary Ed Miliband "sees this as being a good outcome".
The consulate is distinct from the UK embassy in Tel Aviv, which is the UK's main diplomatic hub with Israel.
More on changes at British consulate in East Jerusalem
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