Construction will start on site next year with the store opening planning for early 2013.
The supermarket giant was given unanimous support by the local council to redevelop an empty Hounslow House office block in the centre of the town.
The supermarket development also includes a cafe, independent shops, improved public realm and 285 car parking spaces.
Tesco spokesman Tony Fletcher said: “Tesco has wanted to invest in Hounslow for some time and we are delighted to have worked with the local authority and community throughout this process to gain such strong support.”