The policy, effective in April after a three-month education period, will see "habitually slow players" identified using objective data and penalised for taking too long to hit a shot.
Though the majority of golfers play at an acceptable speed, slow play is a perennial issue, with fast golfers routinely frustrated with their slower-playing competitors.
The tour decided to revamp its policy in August after Bryson DeChambeau was ridiculed on social media when a video circulated of him taking more than two minutes to hit a putt.
"We're looking for guys to take responsibility, because hitting a standard golf shot and taking two, two-and-a-half minutes to play it is not acceptable," Casey told reporters ahead of this week's American Express tournament in La Quinta, California.
Under the new policy, slow golfers will be put on an "observation list" and expected to play their shots in under 60 seconds on average. Those failing to meet the one-minute requirement will receive a warning for their first bad time.
A one-stroke penalty will be handed out for a second bad time, with a further one-shot penalty for each subsequent bad time.
"So taking ownership of that responsibility, however you want to phrase it, that's all about education," said Casey.
Anyone else on the field who takes more than two minutes to play a single shot, in the absence of a good reason for doing so, will be given an "excessive shot time" and if they transgress again will be placed on the observation list.
Englishman Casey, a member of the PGA Tour Player Advisory Council, does not think slow play should be a difficult problem to solve.
"That was our feeling, it should be a fairly simple thing to fix so hopefully this fixes it," Casey said. "Fairly painless gains to be honest."
While the PGA Tour's new policy is still three months away, the European Tour will implement a similar policy this week at the Abu Dhabi Championship. (Reporting by Andrew Both in Cary, North Carolina; Editing by Christopher Cushing)