Murphy, 19, moved to England from Ireland to take part in Chesterfield FC's football and education programme, and has featured for the Spireites’ U19s and U21s.
The teenage forward will be joined at the Proctor Car Stadium by fellow countryman Whelan, who spent time on loan at Pitching In NPL East Division side Sheffield FC last season.
The news comes after talented Gladiators winger Jesurun Uchegbulam took up a full-time footballing opportunity by joining National League Chesterfield last week.
"Kallan Murphy and Leigh Whelan have come in from Chesterfield and have been great,'' Matlock boss Paul Phillips said.
“I’d like to thank Neil Cluxton at Chesterfield for his help."
Photo Credit: Matlock Town