The shutdown has been called by plains-based organisations Amra Bangali, Jana Jagaran and Jana Chetana protesting the move.
Private cars and buses were off the roads, and shops and markets were closed in Siliguri, the plains subdivision of Darjeeling district, official sources said, adding the situation was similar in neighbouring Jalpaiguri district's Malbazar and Alipurduar areas.
Work in tea gardens in the Terai and Dooars, which lie across Darjeeling and Jalpaiguri districts was affected, the sources said.
The bandh is being supported by Akhil Bharatiya Adivasi Vikas Parishad, which opposes inclusion of Dooars and Terai in the GTA.
CPI-M leader Surya Kanta Mishra has said that opposition parties were not consulted prior to signing of the agreement.
Mishra, who is also the Leader of the Opposition in the Assembly, said the nomenclature Gorkhaland Territorial Administration was misleading and confusing and was bound to create disunity in the Darjeeling hills.
The tripartite agreement on the Darjeeling hill authority between the Centre, West Bengal government and Gorkha Janmukti Morcha would be signed today.