Now was “time to turn the page and look to the future”, she said, adding the UK “remains a trusted partner”.
“Parting is such sweet sorrow,” Mrs von der Leyen said.
“To all Europeans, I say: It’s time to leave Brexit behind. Our future is made in Europe.”
Michel Barnier, EU’s chief negotiator
“The clock is no longer ticking,” Mr Barnier said, alluding to the end of the UK’s Brexit transition period on 31 December.
“Today is a day of relief, but tinged by some sadness as we compare what came before with what lies ahead.”
Angela Merkel, German chancellor
Mrs Merkel said the deal had created “the basis for a new chapter of our relationship” with the UK, which will “continue to be an important partner for Germany”.
“The federal government will now closely examine the text of the agreement. But we are not starting at zero. The Commission has kept the member states in the loop during the entirely negotiation process,” she said.
“So we will be able to assess quickly whether Germany can back today’s results of the negotiation,” she added.
Micheál Martin, Irish prime minister
Taoiseach (Irish Prime Minister) Mr Martin said he believed the deal was “a good compromise and a balanced outcome”.
He said there was “no such thing as a ‘good Brexit’ for Ireland”.
“But we have worked hard to minimise the negative consequences,” he added. “I believe the agreement reached today is the least bad version of Brexit possible, given current circumstances.”
Pedro Sánchez, Spain’s prime minister
In a tweet, Mr Sánchez welcomed the agreement but said it would be scrutinised by EU member states in the coming days.
“Spain and the UK continue their dialogue to reach an agreement on Gibraltar,” Mr Sánchez added, referring to the British Overseas Territory on Spain’s south coast.
António Costa, Portugal’s prime minister
“We warmly welcome the agreement reached with the United Kingdom on the relationship with the EU from 1 January,” Mr Costa said in a statement.
“UK will remain, in addition to our neighbour and ally, an important partner.”
Stef Blok, Dutch foreign minister
Mr Blok said the Netherlands would “carefully study the draft texts”, especially the sticking points that held the deal back – fishing, level-playing field rules and governance.
He said there was “very little time to do this” before the end of the Brexit transition period.
“Before a decision is made in Brussels, the government will send an initial assessment of the agreement to parliament, so that it has an opportunity to discuss the agreement.”
Guy Verhofstadt, chief Brexit representative for the EU parliament
Mr Verhofstadt said he hoped the deal “will be a first step in the return of the UK into the European family”.
“Finally a historic and unprecedented deal in the interest of all is reached,” he tweeted. “While less ambitious than we wanted, trough binding arbitration it fully preserves the single market.”
BREAKING: Finally a historic & unprecedented deal in the interest of all is reached. While less ambitious than we wanted, trough binding arbitration it fully preserves the single market. Thanks to @MichelBarnier our Union came out of these negotiations more united and stronger🇪🇺