Clones were phased out of the Stormtrooper Corps and replaced with non-clone volunteers.
Star Wars: Rebels (out-of-universe confirmation)
Pablo Hidalgo has confirmed that the stormtroopers are not clones but are instead volunteers, as of the events in Star Wars Rebels (which occur 5 years before the events of Episode IV). The explanation given is that the production of clones has been phased out, and since the clones age at twice the rate of normal humans1 they are too old to serve as stormtroopers. They have been replaced with non-clone volunteers who are patriotic and loyal to the Empire. Video evidence can be found on Youtube (starting at about 2:56 into the video).
1The clones' age acceleration is not new, but it was not known (outside of Legends) whether production continued after the Clone Wars or not.
Star Wars: Rebels (in-universe confirmation)
One year before The Force Awakens' first teaser trailer was released, the Star Wars: Rebels' sixth episode, Breaking Ranks, main plotline featured Ezra Bridger infiltrating an Imperial Training Academy on Lothal. The fact that Ezra is not a clone and the cadets depicted are all humans of varying skin color and phenotypes demonstrates that the Empire had transitioned to the training of regular citizenry by this point in history.
Tarkin (in-universe confirmation)
The canon novel Tarkin includes an incident where a group of stormtroopers are seen by Moff Tarkin without their helmets. The stormtroopers are led by a Kamino clone sergeant but all the other troopers are non-clone recruits. Here is the relevant quote (the stormtroopers are loading Darth Vader's meditation chamber onto Tarkin's ship):
When the stormtrooper operating the equipment accidentally allowed the
flattened 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.
The novel takes place about 5 years after the end of the Clone Wars, so clone production evidently stopped at the end of the Clone Wars and within 5 years the clones were becoming too old to be useful as soldiers. Hence, they were replaced by non-clone volunteers.