The 55-year-old, who took the reins at the Swansway Chester Stadium in January 2014, has overseen an upturn in fortunes for the Blues in the Vanarama Conference this season following their reprieve from relegation at the end of last term.
Burr agreed to stay on regardless of the outcome at the end of last season and has helped to steer the Blues to mid-table safety with a young, hungry squad packed with potential.
Burr told the club's official website said: “I am absolutely delighted to have extended my contract with the club. I am pleased with the progress we have made from last season. The club has got a fantastic supporter-base both home and away and I firmly believe we have the potential to take Chester FC back into the Football League. I am not saying it’s going to be easy and we have a long way to go but our progress is in the right direction.”
In pictures: memories of the manager's first 12 months at the helm
CFU chairman Grenville Millington expressed his delight at securing the services of the vastly experienced former Kidderminster Harriers and Northwich Victoria manager for an extended term.
"This is a great day for the development of our club and the board's delight in securing this deal will no doubt be shared by fans," said Millington. "The on-field progress this season is there for everyone to see. We are playing attacking football and have secured some tremendous results this season from what is essentially a very young squad. This can only bode well for next season and beyond."
The Blues entertain promotion-chasing Woking on Saturday (3pm).