Clone troopers were almost entirely replaced by human volunteers within 5 years after the end of the Clone Wars.
The canon novel Tarkin shows that most stormtroopers were regular humans and that there were only a few aging clones left (emphasis added):
When the stormtrooper operating the equipment accidentally allowed
[Vader's meditation] sphere to bang against the edge of the cargo hold’s
retracted hatch, Vader stamped forward with his gloved hands clenched.
“I warned you to be careful!” he shouted up at the trooper.
“My apologies, Lord Vader. Wind shear from—”
“Excuses won’t suffice, Sergeant Crest,” Vader cut him off. “Perhaps you are aging too quickly to remain on active duty.”
Tarkin couldn’t make sense of the remark until he realized that Crest’s was a face he had seen countless times during the war—the face of an original Kamino clone trooper. The bare-headed others comprising Vader’s squad were human regulars who had enlisted after the war.
Tarkin, p. 94
Since the human regulars were said to have "enlisted after the war", it sounds like production of the clones ended with the Clone Wars and the Empire began phasing them out immediately.
The five year upper bound is provided by the fact that the novel takes place five years after the end of the Clone Wars and the creation of the Empire:
A long time ago in a galaxy far, far away...
Five standard years have passed since Darth Sidious proclaimed himself galactic Emperor...
Opening crawl for Tarkin, p. 4 (a copy of the opening crawl is also available on Facebook)