The move sent a message that investment in caged farming was a waste of money, she said.
The company's review confirmed the industry needed Foodstuffs to take a clear position on what types of eggs it will need for its future customers so they can plan and prepare.
Many suppliers would need to change the way they farm after heavily investing in colony farming and a realistic timeline was needed to implement the change, Anderson said.
"Foodstuffs believes farmers need to recoup the costs of these investments to allow them to invest further in cage free eggs."
Some suppliers would need to build different types of infrastructure.
"Giving the industry time to achieve this is important as this will ensure our customers' needs can be met," Anderson said.
"On balance we believe 10 years is a reasonable timeframe."
Merchandising teams will gradually reduce the range of caged eggs on offer, before undertaking a promotional programme supporting the transition of the business to cage free over the next few years.
The announcement follows rival company Progressive Enterprises, which owns Countdown supermarkets, announcing its own goal to be cage free by 2025 in March.
That decision came after an investigation by media company Newsroom that Poultry Palace caged eggs were being sold as free range.
Anderson said Foodstuffs had been responding to increasing customer demand for free range eggs for several years.
"Our Pams eggs have been cage free since 2008, and sales of other free range and barn raised eggs have grown significantly over the last decade," he said.
"Now we are ready to take the next step - but we need to work closely with the industry to make this happen.
"Ensuring the correct balance could be achieved both environmentally, and in terms of our egg producers' ability to supply, realise the cost of their investment and manage the retail cost to customers was critical."
Animal welfare group SAFE, which ran a campaign earlier this year lobbying for the end of caged egg sales, congratulated the company on the commitment.
"With both Foodstuffs and Countdown supermarkets going cage-free, approximately 1.25 million hens will be freed from a life confined in cages," SAFE campaigns director Mandy Carter said.
"By law, conventional battery cages have to be removed by egg producers by 2022.
"However, the egg industry was set to replace these cages with equally cruel colony cages."
The decision "hammers a huge nail in the coffin of colony cages", she said.
Carter vowed SAFE would continue fighting for hens until all cages were phased out.
