Earlier this week, the counties voted to play red and white-ball cricket when the season begins three months late, on August 1.
But some disquiet remained over long-form cricket because of the time spent in hotels, which is considered less safe and more expensive.
Fixtures will be confirmed in the coming days.
The competition is in honour of Willis, the great England quick who died last December.
“The commitment of the Chairs and Chief Executives of the First-Class Counties to work together to achieve that ambition has been resolute and we will remain in close discussion as we continue to assess risk factors that need to be mitigated in order to ensure the safety and welfare of their players, coaches and staff,” he said.
“We are all delighted that agreement has been reached across the game and we are now in a position to look forward to and prepare for a new men’s domestic season starting on 1 August.”