David Davis looks ahead.

Foreign Exchange markets saw the pound fall initially on the news of the deal before regaining losses and inching ahead on the morning.

Sterling was up 0.1% against the dollar at 1.34 and up 0.3% versus the euro in early-morning trade.

Craig Erlam, senior market analyst at OANDA, said: "The response in the pound to the announcement may come as a surprise given just how significant today's agreement is, but it's worth noting that this has been in the making over the last couple of weeks and it was in both sides' interest to get this done today.

"Had the two sides failed to come to an agreement then the downside in the pound may well have been far greater. "We've seen a rally in the pound over the last couple of weeks on the expectation of a deal being agreed so what we may be seeing is simply a case of buying the rumour and selling the fact."

Conservative 'remainer' MP, who has been critical of Brexit process, praises PM.

Chris Mason
Political Correspondent

The PM was negotiating all night long with all sides - not only with the EU but Northern Ireland's DUP - about the Irish border.

So talk of progress means there will be massive relief in Downing Street.

This is an absolutely huge moment for them. Let's be clear, it was a humiliation for the PM the other day to find out...that Arlene Foster of the DUP was not going to wear the deal she was about to sign.

Since then, there have been these very, very complex negotiations - multi-national, multi-dimensional, mighty mighty detail, and finally this breakthrough.

But this is just the end of the beginning, because as we move into phase two - the discussions about the future relationship between the UK and European Union - there will come huge political battles and tussles as well.

Today Programme
BBC Radio 4

Image source, Reuters

While the president of the European Council says the progress was a "personal success" for Theresa May, Donald Tusk told reporters the "most difficult challenge is still ahead".

He added he's ready to start preparations for a close relationship on things such as terror, defence and foreign policy but more clarity is needed from the UK for what this will look like.

President Tusk says a year and a half has been spent on "easier tasks" and building a relationship will be "much harder".

Despite progress being made, the DUP says "there is still more work to be done to improve the paper".

Specifically the party says three things need to be focused on:

• the areas of cooperation where it would be necessary to have alignment of rules and standards
• how any alignment could be affected without staying in the single market and customs union
• what necessary alignment may be required to happen

EU chief negotiator enlists help of French decathlete to make his point.

Ireland's deputy prime minister Simon Coveney said the government was content at assurances it had achieved about avoiding a hard border. He said there was now "no scenario" that would result in new border checkpoints. "Ireland supports Brexit negotiations moving to phase two now that we have secured assurances for all on the island of Ireland," he said. He said the deal "fully protected" the Good Friday Agreement, the peace process and an all-Ireland economy.

According to RTE's Managing Director Jon Williams the Taoiseach and Tánaiste will hold a news conference in Dublin on the Brexit deal at 8am.

The Tánaiste spoke on Morning Ireland earlier

The Lib Dems have tweeted their reaction...

Theresa May has now arrived at the European Council for her meeting with Council President Donald Tusk

Image source, EPA

During her speech after the Brussels talks, the prime minister set out her six commitments to Northern Ireland for Brexit.

1. Britain will uphold NI's status as "integral" within the UK

2. The UK will protect Northern Ireland's position in the British single market

3. There will be no new borders in the UK and no hard border between Northern Ireland and Ireland

4. The UK including NI will leave the customs union and the EU single market

5. The Good Friday agreement will be upheld

6. Northern Ireland and the rest of the UK will no longer be subject to the jurisdiction of the European Court of Justice

So what has changed between Monday and today to make the DUP back the agreement?

DUP leader Arlene Foster said the changes made throughout the text "means for me there’s no red line down the Irish Sea."

She said the DUP have been negotiating directly with Prime Minister Theresa May and have had clear confirmation that the entire UK is leaveing the EU, the single market and the customs union.

There were "still matters we would have liked to see clarified," she said, but ran out of time.