The joint venture between the supermarket chain and O2 makes it the largest mobile virtual network operator in the UK with four million customers.
It previously worked with MHP but called a review of its PR agency arrangements, leading to a three-way pitch won by Fanclub.
MHP Brand managing director Rachael Sansom said the agency has worked with Tesco Mobile for three years and came to a "mutual agreement" to part ways.
A spokesman from Tesco Mobile said it is hoping to change perceptions that it is a value, no-frills offering, adding: "Our challenge is to show customers that we offer a service that is not only on par with the established networks, but one that goes beyond that."
Fanclub will work with Tesco Mobile’s social media agency Jam, media planning agency Initiative and above-the-line agency Wieden + Kennedy.