Knowsley Council told CYP Now that it will officially receive the new rating when the full report is published on 13 June, following the general election.
It said it has been informed that three out of the five individual inspection areas have been rated as "good" by Ofsted.
Paul Boyce, director of children's services at Knowsley Council, said: "The feedback we have received reflects the hard work and commitment of our staff and partners in delivering services to our children, young people and families.
"For so many areas of improvement to be identified, together with the acknowledgement that we have completed a programme of significant cultural and structural transformation in children's social care is a great achievement in such as short space of time.
"This really has been a whole-council approach, supported by our partners, with all services playing their part.
"I look forward to building on this success as we continue to further develop our services and ensure our children and families get the best from us in order for them to develop their own potential and prosper."
The last inspection of children's services in Knowsley, the findings of which were published in July 2014, found that too many children and young people who need help and support faced "drift and delay", while some were "left for too long in situations where they have suffered harm".
The re-inspection, which took place in March, found that the quality of leadership, management and governance was "good", with senior leaders and elected members being visible, accessible and well informed.
Meanwhile, the local authority was found to have achieved "significant improvement in social work practice at every stage in the child's journey".
And support for care leavers was also judged to be "good" with those leaving the care system feeling well supported by their personal advisers.