The European Parliament was due to meet on Wednesday afternoon to set the seal on Britain’s departure from the EU.
MEPs were expected to overwhelmingly back ratification of the Withdrawal Agreement, paving the way for the UK to leave on Friday.
It comes after the Withdrawal Agreement Bill completed its passage through Westminster last week.
Mr Verhofstadt tweeted: “The EU and the UK will always need each other. We have gone through a difficult divorce.
“Our main task is now to stay friends and hopefully we come back together in the future.”
The UK’s ambassador to the EU, Sir Tim Barrow, delivered a document called Instruments of Ratification to Jeppe Tranholm-Mikkelsen, the Danish secretary-general of the European Council.
Sir Tim’s Twitter account posted: “This step ensures that the UK has fulfilled its legal obligations regarding our exit from the EU.”
Foreign Secretary Dominic Raab said it would be a “historic moment” and added: “It is the start of a new chapter for an independent, sovereign Britain, looking forward to a decade of renewal and opportunity.
“Whether we are reducing trade barriers between nations, tackling climate change, or improving lives around the world, our vision of a truly global Britain will be a force for good.”
The agreement was signed by the presidents of the European Council, Charles Michel, and the European Commission, Ursula von der Leyen, in Brussels and Mr Johnson in Downing Street.
It settles the terms of Britain’s departure, including future citizens’ rights, arrangements on the Northern Ireland border and the UK’s payments.
It also allows for an 11-month transition period, during which the UK will continue to follow EU rules while talks take place on a free trade agreement.
Mr Johnson wants a deal by the end of the year, but senior EU figures have warned that reaching such a wide-ranging agreement will not be possible within such a tight timetable.
Nigel Farage, leader of the Brexit Party and outgoing MEP, said Brexit was the “beginning of the end” for the European Union. He told reporters in Brussels he would miss being the “pantomime villain” at the European Parliament.