The account was previously held by Wieden & Kennedy Amsterdam.
A spokeswoman for Tesco Mobile confirmed the appointment. She added that the business was handed to SapientNitro as Bartle Bogle Hegarty holds the Virgin Media account.
Tesco moved its £110 million main advertising business to BBH at the beginning of 2015, having worked with Wieden & Kennedy London for more than two years.
SapientNitro also confirmed the win but declined to comment further.
Tesco Mobile launched a TV, online and video-on-demand campaign in September last year using the strapline: "Enough said."
The ads explain how simple its price plans are before using the remaining time to show entertainment.
MediaCom won Tesco’s £90 million media planning and buying business in April, ending the supermarket’s 20-year relationship with Initiative.