I don't know if it ever is stated but the storylines (particularly with the magic tree that was carved into a wardrobe make it obvious that they are the same person.
In The Lion, the Witch and the Wardrobe, Digory appears (not yet named, as the Magician's Nephew was not written yet), at the beginning and the end of the story as the elderly Professor; his house is the place where the Pevensie children are sent as wartime evacuees and enter the wardrobe that leads into Narnia.
The wardrobe was actually carved from the tree Digory planted, after it had been blown down in a storm. Professor Kirke is therefore the first to believe Lucy Pevensie's stories (probably due to his own experiences), though he doesn't tell them why.
In The Magician's Nephew, the sixth book to be published but the first in the chronology of Narnia, Digory is a tall, young teen boy who enters into the newly-created Narnia. While there, however, Aslan sends him on a mission, which allows a magical tree to grow in Narnia which will keep the Witch at bay for nine hundred Narnian years.
He took an apple from this tree, with Aslan's permission and blessing, back to the normal world, and used it to save his sick mother's life; he then buried the core, which grew into a peculiar, and possibly magical, tree in his world.
The tree blew down in a storm at the end of the book; not having the heart to turn it into firewood, he had it crafted into the wardrobe which is the portal to Narnia in The Lion, the Witch and the Wardrobe.
https://en.wikipedia.org/wiki/Digory_Kirke
