The local authority's leadership, the Progressive Alliance, made up of Labour and Lib Dem councillors, claimed in the motion that the privatisation of public transport was "a failed experiment".
There was cross-party support for the plan that could take up to three years to change.
The local authority said thousands of people who rely on the buses were being let down by either strike action or the cutting of routes.
Paul Trendall, Liberal Democrat Progressive Alliance cabinet member for highways, said the authority would take two or three years to change, but the result would be a different model to commercial companies.
"Something more dynamic, something that uses a more agile fleet, more suited to the needs and the routes," he said.
"It is vital we push the government to devolve more powers to the city council so we can operate and manage our own bus services more effectively."
"It seems very easy at the other towns across Milton Keynes to deliver a mix of commercial services but in Milton Keynes it's become impossible to do that.
"We want to understand why and are aiming for a solution to deliver an equitable bus service in every part of Milton Keynes."
"The council running them or franchising them means they can run where people actually need to go," he said.
"There's all sorts of unserved areas in Milton Keynes that the council should and could run a bus service to."
The majority of bus services in Milton Keynes are run by Arriva, which has had to contend with strikes over pay and withdrawal of routes.
However, the operator said: "Arriva has a proud history of serving Milton Keynes in partnership with the council and we remain committed to build on our commercial network through this ongoing partnership - delivering the best possible service to connect the communities of Milton Keynes."
Council chiefs will now write to the Secretary of State for Transport and request an amendment to the Transport Act 1985 to allow it to operate its own buses.