Mr Corbyn was announced as the winner of the leadership election, beating Pontypridd MP Owen Smith, in Liverpool where Labour is gathering for its annual conference.
Corbyn polled 313,209 votes in the Labour leadership election to Smith’s 193,229 votes.
Labour MPs, who triggered the contest with a vote of no confidence, now face the choice of whether to unite behind Mr Corbyn or face further wrath from party members for their stance.
Senior Yorkshire Labour MPs including former shadow work and pensions secretary Rachel Reeves are among those who have always declined to serve in Mr Corbyn’s shadow cabinet while Barnsley East MP Michael Dugher was sacked by the Labour leader in January for apparent disloyalty.
Mr Corbyn has suggested olive branches will be offered after his victory but it remains to be seen who will be invited back into his team and whether they will agree.
Union leaders were among the first to welcome Corbyn’s victory, but said Labour now has a big challenge ahead.
Dave Prentis, general secretary of Unison, said: “Jeremy Corbyn has won because he’s captured the imagination of party members.
“People are inspired by his promises to end austerity, fix our broken public services and build a different kind of economy.
“But the scale of the political challenge facing Labour cannot be ignored. The party already faced an uphill battle to convince the British people before this unhelpful leadership contest.
“A way must be found so Labour can come together - using the talents of the best MPs from across the party in the shadow cabinet, taking the fight to the Tories, rather than fighting one another.
“Jeremy must show those sceptical about his leadership that he has the ability and the ideas to win an election, and enable Labour to regain the support of the British people.”