The club was unable to raise a side for their recent away game at Holker Old Boys Reserves and continued to struggle to get enough players.
Having informed the league on Thursday, league officials have been in discussion with Lancashire FA on how this will affect the current Division Two standings.
The league is aware how a decision on Burnley's previous results will affect both the top and bottom of the division and will communicate in due course.
A spokesman for the league said: "Unfortunately we have now received the written resignation of Burnley United from the West Lancashire Football League with immediate effect.
"This is very disappointing at this late stage of the season but as they are not going to fulfil their two outstanding matches."
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