The intervention comes after Ofsted downgraded the service earlier this month from "good" to "inadequate" - inspectors having found children living in conditions of neglect for "too long".
The move is a blow for the council after it was first to get an "outstanding" rating for its care leavers service in 2015. This part of the service has now been rated "requires improvement".
A key reason for the downgrade was leaders' lack of awareness of the "significant weaknesses" and a "lack of effective management oversight of practice at all levels", Ofsted said in the report.
Ofsted acknowledged changes at the top of the council - with a new council leader and lead member for children starting in May 2018.
There was also an interim chief executive for several months until the role was filled permanently shortly before the inspection.
Ofsted added that the director of children's and adults' services posts have been separated, and managers from within the organisation promoted to take on the acting roles of corporate director of children's services and director of safeguarding.
Regarding the care leavers service, the report stated: "Although care leavers do get some good support, long-term planning is weak and does not ensure that they achieve the best possible outcomes.
"Children and young people are not supported enough to offer feedback or take part in the development of the services that they receive."
The adviser, yet to be appointed, will provide regular progress reports until Education Secretary Damian Hinds decides the post is no longer needed.
Following the damning report, based on findings from an inspection between 4 and 8 March, Trafford Council said it had agreed a series of measures to improve the service.
These include bringing in an audit team to improve quality assurance processes, recruiting additional temporary social workers and family support workers, creating an Improvement Board and developing a full action plan.
Council leader Andrew Weston, admitted the decline in standards was "unacceptable", adding that reversing this was a "top priority".
"I am going to create a dedicated cabinet member for children's social care and this will be led by deputy leader Catherine Hynes, who will offer the leadership, support and challenge the service needs.
"The next step is to set up an improvement board and present our detailed action plan to the DfE and Ofsted.
"We will ensure the improvement of our children's social care services is an open and transparent process."
The DfE said: "The government takes failure in children's service's departments seriously.
"We are working closely with Trafford local authority to monitor their progress and we will appoint an adviser to provide them with the expert advice and support they need to improve.
"We expect most councils to improve with support and challenge from expert government advisers, but we review progress every six months."
The council declined to further comment on the DfE's announcement.