Official sources said the resignation has been accepted.
Shome's exit assumes importance as he was essentially a tax expert and was the main think tank on introduction of the Fringe Benefit Tax (FBT) and the Banking Cash Transaction Tax.
Tenure of Shome, who joined as advisor to Finance Minister P Chidamabaram on October 1, 2004 for three years, was recently extended till October 2009.
Shome was co-convener of a working group on Goods and Services Tax whose report was accepted by official VAT panel.
He was also in the committee working out the rates for GST proposal to be introduced from April 1, 2010.
He was also Union Finance Ministry representative in Empowered Group of State finance ministers on VAT.
With Uttar Pradesh deciding to implement VAT, the new tax system would be implemented across the country.
GST supposed to be extension of VAT to the national level.