The proposal for a new Scottish Professional Football League required the support of 22 clubs, and the motion was passed 23-6 at Wednesday's meeting.
SPL clubs have already backed the revamp, which will mean a renegotiated distribution of revenue and an end-of-season play-off featuring the top division's second-bottom side and the teams finishing second, third and fourth in the second tier.
The current league structure in Scotland will remain the same after plans for a new 12-12-18 set-up were rejected back in April.
SFL president Jim Ballantyne was left with mixed feelings over a decision which means the end of a 123-year-old organisation.
He said: "It is a takeover. We are joining their company, their organisation. They have swallowed us up. We could use nice words about it it, but it is a takeover."
The merger will take effect on June 27, and SFL chief executive David Longmuir said: "I feel there were some reluctant heroes today. There were areas of major concern.
"But nevertheless a lot of them have seen it for the good of the game and we all accept that Scottish football is better governed under one roof."
John Christison, the chairman of Arbroath, admits he was upset to see the demise of the SFL but pragmatic on the reasons for that decision.
Christison said: "I can't say I'm particularly happy, I actually felt quite sick at one stage to that after all these years that's the demise of the Scottish Football League.
"But we really had no option at the end of the day and I think that was the right way to go."
His thoughts were echoed by Hamilton secretary Scott Struthers, who said: "I feel as sad today with the demise of the SFL as a body, and that cannot be forgotten, but equally in terms of positives going forward - after 15 years all 42 clubs are back in the one room again."