Sandwell Council has received back-to-back poor Ofsted ratings and was warned the service could be run externally.
The announcement coincides with the release of Ofsted's latest inspection report which said "positive progress" has been made, the authority said.
Unison said members could be balloted for industrial action if there were "no guarantees around pay and pensions".
Tony Barnsley, Sandwell joint branch secretary, said council staff worked hard protecting children, "many with huge workloads".
More updates on this story and others Birmingham and the Black Country
He said the announcement "put a question mark" over workers' pay and pensions and guarantees were needed from the government.
"It feels like a huge slap in the face really," he said.
"Members have already indicated about action for a ballot to strike and if we don't get the guarantees we'll be faced with little choice but to go for the ballot process."
Councillor Simon Hackett said the council did not agree with the trust model, but accepted the decision.
The move follows a government warning last December that failing departments would have six months to improve or be taken over by high-performing councils or charities.
Sandwell's children services was rated inadequate in June last year after another poor rating in 2013, which led to two resignations at the authority - a department boss and a cabinet member.
Analysis: Rob Mayor, BBC WM Black Country Political Reporter
This isn't the first authority to have a trust appointed - councils in Slough, Doncaster and just down the road Birmingham have all gone through the same.
But this is another blow for Sandwell Council which last year said it "struggled to see how Ofsted came to the conclusion" that it's children's services were inadequate.
The councillor in charge of the department Simon Hackett, who's previously ruled out resigning, says he doesn't think a trust is the best way to improve services, but making it a success is his "priority".
Behind the scenes there are concerns about morale of staff in a department which has been under siege since an inadequate rating three years ago.
Today the council is saying everything it can to reassure them as the trust takes over.
Earlier this year, Children and Families Minister Edward Timpson announced Eleanor Brazil would be the new commissioner of children's services at the council.
She recommended appointing a trust, he said.
Mr Hackett, cabinet member for children's services, said he was disappointed with the decision and improvements had been made which were reflected in Ofsted's latest report.
He added: "However we know there is more to do to improve the quality of social care and accept we must accelerate the pace of change. For this reason, we acknowledge intervention can help us reach the high standards we are determined to achieve.

John Russell Brown and his company Hyperion Investments face 16 charges relating to the condition of the property and the danger and risk to health of the occupants in it.
The migrants were found during a raid on Deeside Lane, Sealand - one of the largest of its kind in the country.
Magistrates in Wrexham adjourned the case until 10 December.
A struggling children's services department is to be taken over by a government-appointed trust.
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