Some staff at the charity, whose patron is Prince William, had voted to walk out over planned pay cuts and redundancies.
Unite represents 88 out of 212 Centrepoint employees. Of those staff, 20 voted in the ballot, with 11 in favour of strike action.
But the charity and union announced today the dispute had been settled after discussions with the conciliation service Acas.
The main points of the agreement include: a no compulsory redundancy policy; an agreed job restructuring policy; a 5 per cent reduction in salaries, capped for 15 months, rising to no more than a 10 per cent reduction after that date; and confirmation of a 37.5-hour week.
Seyi Obakin, chief executive of Centrepoint, said: "We regret the need to restructure but are pleased to have reached an agreement with Unite and its members.
"We can now ensure the long-term existence of Centrepoint and continue to help homeless young people."
Unite regional officer Matt Smith said its members "overwhelmingly supported" the offer.
"We believe this was the best deal possible we could have achieved for our members working for this iconic charity," said Smith.
"We are pleased that Centrepoint’s management listened to Unite and stepped back from the brink."
Centrepoint management originally proposed to increase the week to 40 hours, make 34 redundancies and cut some employees’ salaries by between 15 per cent and 36 per cent.
Unite members voted to strike in September, but Centrepoint hired law firm Eversheds to prevent action by declaring the ballot had not been properly conducted.
The union then reballoted members, who voted in favour of strike action.