UPDATE: This article originally stated that Mr Healey contacted Cow & Gate to make a complaint. We have since learned the Healey family contacted Tesco not Cow & Gate. The story has been updated to reflect this.
Claire Healey, 30, and husband Ryan, 34, bought a box of Cow and Gate porridge from their local Tesco Express on 7 January, only to discover the product expired in March 2014.
They realised it only minutes before feeding it to their seven-month-old son Rupert.
Mr Healey, from Bingley, West Yorkshire, said: "I dread to think what would have happened if we had actually fed it to my son. Sell-by dates are there for a reason - it's disgusting that this has happened."
The couple said they only thought to check the date at the last minute as the box appeared worn.
They said Rupert has been having the same particular porridge for breakfast since he started eating solids.
Mr Healey said: "It's bad enough for an adult to eat food that's far out of date, but for a child so small it's scary.
"The worst case scenario doesn't even bare thinking about.
"It's not just that it's two years out of date. I went back the next day for some more and the sell-by dates on those boxes were in 2017, so that particular box has probably sat on the shelves for at least three years."
Mrs Healey said she wants more parents to be aware about checking for dates on food for their babies.
She added: "It has certainly made me paranoid about sell-by dates. I just feel really lucky that we noticed it in time."
After contacting Tesco, Mr Healey said they have been offered vouchers worth the value of the refund, but this isn't satisfactory.
He said: "It isn't about the refund. It's about making people aware of the situation and making sure it doesn't happen again.
"It shouldn't have happened in the first place.
"I feel their response was very robotic. I understand they have a standardised response but for an incident like this I feel they should have gone above and beyond and they haven't really.
"Sometimes you see pictures of flies in fruit and stuff that has been damaged beyond their control, but this is their error."
A Cow and Gate spokesperson said: "We're concerned to hear about Healey family's experience.
"If parents ever have problems or questions about any aspect our products, we are always available with help and advice from our Careline."
A Tesco spokesperson said: "We are committed to the highest standards of food safety for our customers and we have robust procedures in place for the rotation and date code checking of our products.
"We're sorry that we did not meet these standards in this case. We have checked the shelf life of the baby products in our Crossflatts Express store and all products are comfortably within the sell by date."