Last month, the Scottish Premier League decided to seek the expansion of their membership, with a proposal to split the two leagues into three divisions of eight after 22 games.
After Monday's three-hour meeting at Hampden, SPL chief executive Neil Doncaster revealed there had been full support for a new "24-18" team model.
This would involve the top flight divided into two divisions of 12 teams. The '18' refers to the remaining Scottish Football League clubs not included in the top leagues.
Doncaster told Sky Sports: "I'm delighted to say that we have unanimous agreement in principle from the 12 SPL member clubs to the 24-18 team model.
"We are looking forward to sitting down with the Scottish Football League and the Scottish FA to talk about the details.
"What we aim to have is a consensus model that cares for all of Scottish football and that's got to be the objective going forward."
These proposals will now be discussed with the SFA and SFL on Thursday.
The SFL's 30 clubs have previously voted in favour of three leagues, comprising of 16, 10 and 16. The SPL has spoken informally to SFL clubs and it is felt there is sufficient support for the changes.