The authority said the service would be replaced by a volunteer-run "home library service" for people who are unable to access a public library.
Three mobile library staff members have taken voluntary redundancy and talks are on-going with four others.
The current service will end after 30 June as the authority looks to save ??1.7m by 2020.
In its report, Hampshire County Council said it would look to develop links with voluntary groups which provide community transport to help people in rural areas access their local library.
The decision to scrap the service follows a public consultation which sawa more than 9,500 people and organisations respond.
Plans to close the mobile service in Grayshott less than a year after its static library was shut "raised dissatisfaction" with residents and organisations, the council said.
Other concerns raised included children not having access to books.
However, the council said 62% of respondents were in favour of stopping the service - which is used by 1% of total library customers and costs ??11.44 per visit, per customer, compared to ??2.23 at static libraries.
Hampshire's mobile library service is to be scrapped, the county council has confirmed.