The European Parliament approved the Brexit Withdrawal Agreement with a majority of 621 votes to 49 in Brussels on Wednesday evening.
Following the vote, other MEPs began singing Auld Lang Syne as a symbolic send-off for the UK’s 73 MEPs leaving their roles.
The vote paves the way for the UK to leave with a deal in place on Friday 31 January, at 23:00 GMT.
Upon signing the letter giving the EU’s approval to Brexit, European Parliament president David Sassoli said: “You [the UK] are leaving the EU but you will always be part of Europe…it is very hard to say goodbye.
“That is why, like my colleagues, I will say arrivederci.”
Sassoli added that the UK's exit was "painful" for the EU, but urged that focus on building a positive future relationship must now follow.
Echoing the words of late Labour MP Jo Cox, he said: "there is more that unites us than divides us".
European Commission president Ursula von der Leyen also called for the EU and UK to "join forces" ahead of future talks, emphasising that the Withdrawal Agreement was only the "first step" in deciding their future relationship.
Von der Leyen added: "We will always love you [the UK] and we will not be far".
The European Parliament's Brexit spokesman Guy Verhofstadt added that it was "sad" to see the UK leaving having "twice given its blood to liberate Europe", paying tribute to the UK's MEPs whose "wit, charm and intelligence" would be missed in Brussels.
Conservative MEP Daniel Hannan said that the EU was "losing a bad tenant and gaining a good neighbour".
Hannan informed the chamber that when it became clear that "the aspiration was to have the EU as a quasi-state", British sentiment grew increasingly eurosceptic.
He said: "If at any stage Britain had been able to have a trade-only relationship that would have been enough."
Meanwhile, in his final speech as an MEP, Brexit Party leader Nigel Farage said: "I want Brexit to start a debate right across Europe - what do we want from Europe?"
Criticising the EU, Farage insisted that "trade, friendship, co-operation and reciprocity" among nations was possible without "all of these institutions and all of this power".
He and his fellow Brexit Party MEPs then waved Union flags in the chamber before staging a walk-out.
Following the UK's departure on January 31, the 11-month Brexit transition period will begin, during which the two sides will commence negotiations over the future economic relationship.
Talks relating to a future trade deal are expected to begin in March.
