MEPs ratified the Brexit Withdrawal Agreement by 621 votes to 49 following an emotional debate in Brussels.
After the vote, MEPs marked the UK's exit by singing Auld Lang Syne.
Several British MEPs said they hoped the UK would return one day although Eurosceptics, including the Brexit Party's Nigel Farage, used their final speeches to tear into the EU.
The UK is due to leave the bloc at 23:00 GMT on Friday.
Ratification of the withdrawal agreement, agreed by the UK and EU in October, was not in doubt after it easily cleared its committee stage last week.
Signing the letter confirming the EU's consent, the Parliament's president, David Sassoli, said the two sides must heed the words of the late Labour MP Jo Cox when approaching their future relationship and recognise "there is more that unites us than divides us."
"You 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."
Wednesday's session saw those on either side of the Brexit debate, including the UK's 73 MEPs, celebrate or lament the end of British EU membership.
Some MEPs marked the occasion with songs - others wore "always united" scarves.
The Parliament's Brexit spokesman, Guy Verhofstadt, said it was "sad to see a country leaving that has twice given its blood to liberate Europe".
He added that British MEPs had brought "wit, charm, and intelligence" as well as "stubbornness", and would be missed.
President of the European Commission Ursula von der Leyen said ratification of the withdrawal deal was "only a first step" towards a new partnership between the EU and the UK.
The two should "join forces" in areas such as climate change, she said, and seek a close partnership following the UK's exit on Friday.
"We will always love you and we will not be far," she told the UK in closing.
The EU's Brexit negotiator Michel Barnier also wished the UK well, saying the bloc would approach talks on the future relationship with "patience" and "objectivity" while defending its members' interests.