The firm had raised an action at the Supreme Court in objection to a site near its Rousay Drive store. The site was being zoned for retail use, allowing the potential for a rival to move in.
However, on Tuesday, Tesco confirmed it had withdrawn its legal challenge.
The announcement was welcomed by Aberdeen City Council.
Council Leader Barney Crockett said: "Aberdeen is an economic powerhouse. It is attracting international attention from investors and businesses, which see the opportunities this flourishing city can offer and they want to take advantage of those opportunities.
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"Nevertheless, the Tesco challenge to the Local Development Plan could have undermined developer confidence in the city and it is impossible to say how much damage these spurious court actions have caused.
"I am confident, however, that damage can be repaired and that the abandonment of the legal challenge can only serve to further boost confidence in Aberdeen as a can-do city which offers fantastic development and growth opportunities to businesses across the spectrum and that developer confidence in our city will be fully restored.
"We hope that a line has now been drawn and we can restore normal relations with Tesco."
Development Management Sub-Committee Convener Councillor Ramsay Milne added it was "unfortunate" that Tesco had "decided to attack development and economic prospects for the whole of the city by attempting to have the entire Local Development Plan quashed rather than simply challenging the part of the Plan with which the company disagreed".
The Aberdeen Local Development Plan was formally adopted in February 2012. It was the first in Scotland to be approved and adopted under new legislation. It sets out the Council's priorities for regenerating parts of Aberdeen and for supporting a thriving city centre, as well as creating a blueprint for the development of the city over the next decade.
(JP/MH)
