Foremost School near Harrogate was placed in special measures by Ofsted last year.
North Yorkshire County Council approved plans to turn it into a special co-ed day school at a meeting earlier.
It comes after the authority failed to attract a suitable independent provider to run the school.
A report to the executive board said: "Officers have continued to place the best interests of pupils, current and future, at the centre of their thinking.
"The way forward should offer the best possible outcomes for children and young people.
"This means making a realistic commitment first of all to the school coming out of special measures by March 2015."
Foremost School opened in 2012 to cater for boys who were removed from mainstream education because of difficult behaviour.
But concerns were raised last year about the quality and sustainability of the school.
Plans were made to find an alternative provider in January but the authority only received one bid for the contract - which was not of "high enough quality".
A consultation conducted at the same time found there was less demand for residential places, but day places continue to be needed.
Final approval on changes to the school, which currently has 10 pupils, will be made in September once a legal notice period has expired.
A failing boarding school in North Yorkshire for boys with behavioural problems is to be turned into a mixed day school.