On the eve of the BMW Championship at Conway Farms near Chicago, Day said Swatton had been a "bit shocked" at the news, after carrying the 29-year-old Australian's bag for all of his career.
"Unfortunately it just didn't work out," Day said. "I'm trying to find my footing here. I had to do it at some point."
Day's dominance from late 2015 through the first half of 2016 saw him capture a first career major and rise to number one in the world.
Day said Swatton would remain as his coach, but his friend, Luke Reardon, will be on the bag this week.
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"He's not out of my world one bit," Day said of Swatton. "I'm hoping things move forward with us like they always have ... Because we both love each other like family."
In June, five-time major winner Phil Mickelson split with caddie Jim "Bones" Mackay after 25 years.
And last month former world number one Rory McIlroy parted with his longtime caddie J.P. Fitzgerald.