In what is seen as the latest chapter in the long-running Brexit saga, the leaders are due to vote on the draft texts agreed by both sides after months of complex and arduous negotiations.
The UK is due to leave the EU on March 29, 2019.
Here, Al Jazeera takes a look at what to expect at the key Brussels summit.
The deal consists of two separate documents which have been drafted and agreed by negotiators from the UK and the EU in the past two weeks.
The first one is the withdrawal agreement, also known as the “divorce” deal. This document sets out the terms of Brexit in the wake of a landmark June 2016 referendum, which saw 52 percent of voters opting to leave the club the UK had joined in 1973.
At 585 pages long, it is by far the longer of the two documents on the table on Sunday.
The legally binding text deals with a number of issues, including citizens’ rights, the so-called “divorce settlement” and a mechanism to prevent a hard border between Ireland and Northern Ireland being implemented in the future, known as the “backstop”.
It also includes details on the length of Britain’s transition period, whereby no major changes will be made to the UK-EU relationship, as the two parties work out a post-Brexit trade deal.
That period is currently set to last from March 2019 until December 2020, although the length of the transition could change at Sunday’s summit.
The second document is the political declaration, an aspirational, non-legally binding text that sets out the terms of the future relationship between the EU and the UK over 26 pages.
It deals with ambitions for a future trading relationship, as well as close ties on foreign policy, criminal justice, law enforcement, security and defence.
The leaders of the EU member states are due to vote on both texts.
In the days before the summit, some states raised objections regarding the content of the withdrawal agreement, including over the issue of fishing rights in the UK’s territorial waters post-Brexit.
The Europeans want to secure the same access to fishing waters around Britain that they currently enjoy, and have tried to tie the issue to a future trade deal with it.
Not by a long way.
The British Prime Minister Theresa May will still have to get the deal approved by the UK parliament, where she faces a formidable task to win a majority in the 650-member House of Commons.
Domestically, the prime minister’s draft deal has been attacked from all sides. Dozens of May’s 315 Conservative MPs are expected to vote against the deal, as is the opposition Labour Party.
Northern Ireland’s Democratic Unionist Party (DUP), which props up May’s coalition government with 10 MPs, has also indicated it will vote against the deal. On Saturday, the DUP urged May to “bin the backstop”.
The parliamentary vote is likely to take place in early-to-mid December.
If the UK parliament approves the deal, which seems unlikely, then the British government would propose new legislation in January, which would then need to be approved by parliament before it becomes law. It would then need to be ratified by the EU before Brexit Day on March 29.
If MPs in the UK reject the deal, as seems highly likely at this stage, then a number of scenarios could play out.
Jeremy Corbyn’s Labour would likely push for a general election to be held as soon as possible.
Conservatives could look to either unseat May as leader of the party, or try and amend the Brexit deal before bringing it for a second vote in parliament.
Meanwhile, campaigners for a second referendum on Brexit would likely also intensify their efforts to secure a new public vote, including the option for the UK to remain in the EU.
It remains to be seen whether politicians or the public have the appetite for a second referendum.
With Britain scheduled to leave the EU in March, there will not be much time for British leaders to act. If the UK reaches that date without a deal in place, then it will still leave the EU.
A so-called “no-deal Brexit” is widely predicted to prove catastrophic for the UK and is seen as an option that pretty much all sides are desperate to avoid.