French President Emmanuel Macron has praised the EU's histoic deal, saying "there is no such thing as a perfect world, but we have made progress".
He said the deal followed long and difficult negotiations, during which concessions had to be made to win over member states whose objections blocked the deal.
But the concessions were necessary to deliver a recovery plan big enough to be effective, he added.
"Never before did the EU invest in the future like this," Belgian Prime Minister Sophie Williams said.
The 27 leaders were said to have bumped elbows and made jokes before finally approving the deal.
"An extraordinary situation demands extraordinary efforts," said German Chancellor Angela Merkel.