Preheat oven to 425° Fahrenheit. Line baking sheet with parchment paper and set baking sheet aside.
Add shredded chicken, chopped celery, chopped green onion, and buffalo sauce to large mixing bowl. Stir until ingredients are fully incorporated.
Spread egg roll wrappers out on flat work surface, with wrappers rotated to create diamond shape with one corner pointing up at top, rather than square shape with flat edge across top.
Working with wrappers one by one, place ¼ cup buffalo chicken filling across center of egg roll wrapper.
Fold bottom corner of egg roll wrapper up and in toward center to cover buffalo chicken filling. Fold left and right corners of egg roll wrapper up and in toward center to cover bottom corner. Note: for more secure egg roll, dampen fingers with water and lightly moisten each edge of egg roll wrapper before folding.
Starting with bottom edge of egg roll, carefully roll egg roll tightly from bottom edge toward top corner. Note: for more secure egg roll, dampen fingers with water and lightly moisten top edges of egg roll wrapper before folding.
Place rolled and sealed egg roll on baking sheet lined with parchment paper. Repeat process until all egg roll wrappers have been filled, rolled, and sealed.
Place baking sheet in preheated oven. Bake egg rolls 15 to 20 minutes, or until egg rolls are golden brown and crispy, being careful not to burn wrappers.
When egg rolls are baked to preferred doneness, carefully remove baking sheet from oven. Transfer egg rolls to serving tray or plates and serve hot with ranch or blue cheese dressing for dipping, celery sticks, and carrot sticks, if desired.