Councillors appointed corporate director Kate Page as interim chief executive.
Mr Best's resignation follows a row about the council's education building programme.
He has been at Milton Keynes for 11 years and in the top job for five.
Mr Best said: "I am tremendously grateful for the opportunity to have led the council at such a critical and exciting time in its evolution."
Council leader Isobel McCall (Lib Dem) said: "John has been an extremely dedicated and enthusiastic chief executive who cares passionately about the council and Milton Keynes. He has been central to our improvement journey."
A council statement added: "John has been a major influence in helping the city find its way into the 21st century, working with boundless energy and commitment to actively promote MK's national and international profile in preparation for the city’s significantly increased influence in the future.
"At the same time, under his stewardship the council has won a number of national and regional awards and can point to steadily increasing citizen approval."
Ms Page is corporate director for neighbourhood services, having joined Milton Keynes in 1999.
Previously she worked for Kirklees and Wigan MBCs, Northamptonshire CC and Scottish Borders Council.