BBC Monitoring

A quick look at how Jeremy Corbyn's victory is going down in other countries. Announcing the result, both Russian state-owned TASS news agency and privately-owned Interfax news agency recalled his recent statements to the media that he wants the UK to show more respect in building relations with other countries, in particular, Russia.

More from Allegra Stratton and the Newsnight team at Newsnight Live

Laura Kuenssberg
BBC political editor

Image source, AP

He, and they did it. Now what?

Jeremy Corbyn's victory was not the work of Labour MPs, power brokers, or the party's once powerful machine. But the flex of an old muscle - Labour's left-wing rump - once so weakened, now strong, emboldened by thousands upon thousands of new supporters.

They will have their celebrations tonight - deservedly so. Corbyn has achieved a rarity in modern politics - expanding an electorate. Persuade more people who agree with you to take part, and you can win, however out of fashion those ideas are.

But now installed, there are problems everywhere for Labour's new leader. He has always been an outsider, an insurgent in his own party.

Read more from Laura.

Reacting to Jeremy Corbyn's election, the Institute of Directors congratulates the left-wing MP but says some of his policies - such as renationalising the railways and increasing government spending - "would undermine our open and competitive economy". Director General Simon Walker says businesses will put their case to Labour, and "we very much hope the Labour party will be prepared to listen".

Sinn Fein president Gerry Adams has passed on his "warmest congratulations" to the newly-elected Labour leader.

Former Scottish First Minister Alex Salmond - now an SNP MP - tweets his congratulations to the new Labour leader.

Tom Watson tells the BBC that he has hardly seen Jeremy Corbyn over the last three months and the first time he sat down for a chat with him was after the result was announced. He says a reshuffle will now take place, adding that his advice to his new leader is to "take your time and to start with the top jobs and work your way down". On his role, he says his main task is to make Jeremy Corbyn's "very different vision for change" a reality in the run-up to the 2020 election and to overhaul the party's campaigning. He adds:

BBC Newsnight

Jeremy Corbyn got 251,417 votes in this contest. By way of comparison, that's over 50,000 more than David Cameron and David Davis got combined in the final round of the Tory leadership contest of 2005. More analysis at Newsnight Live

BBC Radio 5 Live

Shadow cabinet ministers Rachel Reeves and Jamie Reed have resigned their frontbench roles following Jeremy Corbyn's win - but shadow minister for small businesses Toby Perkins says he'll "stick around and fight". 

Lord Prescott hails a "remarkable day" for Labour and says the party has been totally transformed in the past four months. He praises Mr Corbyn's acceptance speech, saying it spoke "to the heart" of Labour members, contrasting it with Tony Blair's "new dawn" rhetoric when he won the 1997 election. He urges those thinking of resigning from the shadow cabinet to think again, saying the party has "overwhelmingly endorsed" Mr Corbyn who he says got more votes than Mr Blair when he won the leadership in 1994. His message:

Diane Abbott, an early backer of Jeremy Corbyn, tells the BBC that he has an "overwhelming mandate" and it was "really important" that he won in every section of Labour's electoral college - party members, registered supporters and affiliated supporters. She says Labour must harness the enthusiasm of the young people who have flocked to Mr Corbyn to build an election winning platform in 2020. She says Mr Corbyn will assemble a "very talented" team from within the ranks of Labour MPs. Asked whether she will serve, she insists she is a "happy backbencher". 

BBC News Channel

Labour leader Ed Miliband congratulates Tom Watson and Jeremy Corbyn on their victories. He says he'll be offering his support to Mr Corbyn and hopes the rest of the party does the same. He says Mr Corbyn had a solid victory, and his mandate should be respected. But he hopes the left-wing MP will reach out to all parts of the party, saying he has a "big job" to unite it.

"This is a big opportunity for us," Mr Miliband adds. He says Labour's membership is now more than 500,000, and the task ahead is to ensure those members form an "active part" of the party. He also defends his decision to resign in the immediate aftermath of May's election, saying it was the right thing to do. Mr Miliband says he will remain as a backbench MP to campaign on inequality and climate change.

Rachel Reeves says she will return to the backbenches when she comes back to work after maternity leave in January. Ms Reeves, who has been shadow work and pensions secretary, says Jeremy Corbyn has a huge mandate from the party and she wishes him well, but he needs to appoint a shadow cabinet that shares his vision. She says she has too many policy differences with him. 

BBC Radio 5 Live

Copeland MP Jamie Reed - who has resigned as shadow health minister immediately after Jeremy Corbyn's election - says he will still work with the party's new leader: