Jung had rejected the recommendation of the outgoing AAP government that the Assembly be dissolved.
The Cabinet decision will come into effect after promuglation of a notification by the President.
It has to be then got endorsed by Parliament through a resolution under Article 356 of the Constitution.
In a report to the Centre, Jung did not favour dissolution of the 70-member Delhi Assembly as recommended by the council of ministers headed by Arvind Kejriwal when it met last night and decided to quit.
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Sources said Jung has conveyed to the Centre that the national capital be brought under a spell of President's rule as no party is now in a position to form an alternative government.
The final call on the LG's recommendation will be taken by the Centre, the sources said.
Home Ministry officials said they would take the opinion of the Law Ministry and place all the facts before the Union Cabinet for the final decision.
The Assembly elections late last year had given a split verdict with no political party getting absolute majority. The Aam Aadmi Party led by Kejriwal formed the government in December with Congress support.
The LG has also sent, along with his report, the resignation letter of Arvind Kejriwal. The letter would be forwarded to the President for its acceptance.