The Yorkshire authority has been rated "requires improvement" for overall effectiveness following an inspection in June. It received the same rating for the key areas of leadership, child protection work and services for looked-after children.
In a letter detailing the findings, lead inspector Lisa Summers said: "Since the last Ofsted inspection in September 2016, when the local authority was judged inadequate overall, strong and resilient senior leadership has underpinned the improvement in practice from a considerably low base."
Summers added that the pace of change was initially slow but that steady progress has been made since March 2018 when a formal arrangement with Leeds City Council taking responsibility of overseeing improvement was put in place by the Department for Education.
She said: "Children who need help and protection are now recognised, and risk of significant harm is quickly responded to."
The report identified several areas where things still need to improve, including "the quality of recording, assessments and child protection investigations so that children receive help at the earliest opportunity".
The responses to disabled children, children in private fostering and children at risk from professionals where allegations had been made also need to improve, the report states.
When children go missing from home and care the quality of return home interviews still need to be improved "in order to better understand why children go missing and to inform care planning and strategic priorities" it adds.
Other practice requiring improvement includes the quality of foster care reviews, management and oversight through improved performance and quality assurance, and regular supervision of social workers "that is refective, directive and, alongside the work of independent reviewing officers, challenges poorer practice".
However, the overall tone of the report was positive. Summers said: "There has been steady and continuous progress to improve the intial response to children in need of help and protection."
The report also notes that staff stability and "confidence in core social work practice" have significantly improved since the last inspection, and that the council "nurtures and develops its new social work staff".
Mel Meggs, Kirklees' director of children's services, said: "We are pleased that Ofsted have recognised the real progress that has been made across the board. This has been achieved by hard-working staff and committed partners and means we are in a strong position to continue our improvement programme.
"The Ofsted report also outlines a number of areas for further improvement. We are already making good progress with these changes and our ambition is to be judged 'outstanding' in the next Ofsted inspection.
"We have a dedicated and hard-working team who care passionately about those they care for and support. It is thanks to them that we are seeing the steady improvements we are making."
The positive findings come in stark contrast to the disharmony in the department two years ago. Then, Unison organised a 48 hour strike by children's social workers who were unhappy over pay, heavy workload and bullying.
*The latest monitoring visit to Croydon Council's "inadequate"-rated children's services has also noted improvements.
The Ofsted report, based on a visit made in July, states: "Children and young people are beginning to receive a better quality of service, and the pace of improvement is accelerating.
"In a relatively short period of time, the new executive director and the director of early help and children's social care have improved morale, raised the visibility and impact of leaders and managers, started to embed a practice model and created conditions that are enabling steadily improving practice and outcomes for children."