Cowdenbeath will now host Arbroath in the first fixture of the new football season.
The club were promoted to Division Two after Livingstone were relegated two leagues by the SFL.
The West Lothian club, now run by a consortium led by former Cowden chairman Gordon McDougall, breached rules relating to insolvency.
Cowdenbeath narrowly missed out on a Second Division spot on merit after leading the third tier for a large part of last season.
A late surge by their rivals left them with only a play-off place and, after reaching the final, they were beaten in a penalty shoot-out by Stenhousemuir.
Manager, Danny Lennon, said, "This news is a massive lift for everyone at the club, the players, the supporters and the community.
"It was very disappointing to lose in the play-off final and we know it is going to be difficult task now next season, but it is certainly not beyond our players."
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