LONDON — It’s done. At last. The European Union gave its final, formal approval to Brexit on Thursday, clearing the way for Britain to reverse 47 years of integration with the Continent and leave the bloc on Friday night.

Following a sometimes emotional vote in the European Parliament on Wednesday, the governments of the 27 countries still in the union gave a unanimous seal of approval to Britain’s withdrawal, officially ending nearly four years of impassioned wrangling over whether, when and how it would happen.

[Just get on with it, says Britain. Remainers are girding for the next fight.]

In the end, the way the decision became final was vintage Brussels: bureaucratic and undramatic.

Diplomats from the remaining member countries were given plain instructions over email just after 8 p.m. Wednesday: Answer these four dry, procedural questions with “yes,” “no,” or “abstain” and send them in an email to the European Council, which represents the 27 nations’ governments.