Macron addressed the press at the end of the meeting, calling the conclusion the "best compromise possible", adding that the October 31 deadline "protects us", because it was "a key date, before the installation of the new European Commission".
Britain was hoping to leave on March 29, then April 12.
The UK must now hold European elections in May, or leave on 1 June without a deal.
She said lawmakers should reflect during their forthcoming Easter break on the decisions that will have to be made swiftly upon their return.
And she said if Mr Corbyn got into power it would mean "destroying our defences, abandoning our allies, billions more in borrowing, fewer opportunities, and higher taxes for everyone". The choices we now face are stark, and the timetable is clear.
- How will the delay go down with her party?
They fear that the delay might be prolonged yet again - and the extra time used to engineer a softer form of Brexit, or even see it annulled outright.
But she added that she would she would seek more talks with Jeremy Corbyn today - but would not be drawn on when she planned to quit as former leader Iain Duncan Smith said she must stick to her promise to resign next month while veteran Brexiteer MP Sir Bill Cash said Mrs May must go immediately.
Mrs May replied: "Can I agree with you that I believe a Conservative Government will make a success of whatever the situation is in relation to Brexit?" Under party rules, she's technically safe from a leadership challenge until the end of the year. The pound was unchanged on the news, as investors had priced in an extension.
The delay allowed traders to breathe a sigh of relief but observers noted the reprieve was only brief with the agreement merely kicking the can down the road.
British Prime Minister Theresa May speaks at a news conference at the conclusion of the European Union summit in Brussels. Most member states entered the meeting in support of a longer extension of variable durations - up until March 2020 in some cases - but French President Emmanuel Macron took a tough line to demand a short extension until June.
He said communities across the country have been "abandoned", adding: "Official figures show that nine of the 10 most deprived council areas in this country have seen cuts nearly three times the average of any other council".
However, it could mean Britain having to take part in European Union elections scheduled in May, and there are still few signs that lawmakers will vote on Prime Minister Theresa May's Brexit deal, further prolonging the political chaos.
Earlier, in a letter to Sir Graham, Dr Fox said continued membership of a customs union would leave the country "stuck in the worst of both worlds".
Manfred Weber, a German who leads the biggest group in the European Parliament, said Europe showed "patience and unity" in avoiding a damaging no-deal Brexit.