The 21-year-old striker joined the Magpies at the end of November and he will now remain with the League One club for the remainder of the season.
Ball suffered a bout of concussion recently but he will be back in the squad for Saturday's home game against Sheffield United.
"Derby have been great and Steve McClaren has fully acknowledged what we are trying to do here," said Notts boss Shaun Derry.
"One or two other clubs were interested in signing Callum so for him to choose Notts County shows he believes in what we are trying to do here."
The Magpies are also looking to extend Callum McGregor's loan from Celtic, which expired last weekend, but other clubs are interested in the midfielder and the Scottish champions have yet to make a decision on the 20-year-old's future.