The brief will support a wider marketing plan covering brand campaigns aimed at building greater emotional engagement and relevancy with Three's target audiences.
In addition, Cow will be responsible for launching all new products and services together with supporting the Three press office.
Cow MD Lisa Taylor, who leads the account, told PRWeek the company was looking to move beyond a focus on the tech market.
"We will be targeting both high-end trendsetters and those who won’t pay for top end phones but want to understand what a mid-range phone can do for them.
"A focus on tech will still be important but Three is moving more into the mainstream, and this will be about us taking them into a new space as a challenger brand with a feisty mentality."
This will mean increased efforts to get into the consumer, lifestyle and news pages, she added.
Georgie Carter, head of consumer PR at Three, said: "We have huge ambitions for our brand and we need an agency that will push the boundaries in terms of creativity. Cow PR really delivered on this brief and proved it has the ability to set us apart from the competition."
The pitch, handled by AAR and thought to be worth a six-figure sum, followed the company parting ways with incumbent 3 Monkeys.