Lauren Hartley, 26, and Luke Hewick, 28, were walking by a bin in Kingswood, Hull, when they heard tiny cries for help.
They peeked inside the trash can and noticed that an Asda bag was rustling, so quickly fished it out of the rubbish.
To their surprise, two frightened kittens were shivering inside.
The couple took the wet moggies home and reported the incident to the RSPCA, who are investigating to find out exactly what happened.
Lauren and Luke have since adopted the adorable pair, who are thought to be around eight weeks old, and named them Roscoe and Cooper.
Luke said: ‘We had just gone for a walk, and we wouldn’t normally go down that way, but Lauren said we should just for a change.
‘We had stopped nearby to stroke a friendly cat and then carried on walking when we heard some little miaow cries, so I thought the cat had followed us.
‘I turned around and couldn’t see anything and then Lauren said the sound was coming from around the bin.
‘Then she saw the bag inside the bin move, so I tentatively put my hand in and pulled out the Asda Bag for Life.
‘I untied it and there was another bag tied up inside – then I opened this and found the terrified kittens.
‘They were shaking and scared and soaking wet. I am not sure if it was because of the storm which we had before we found them or if they were wet from breathing in the bag.
‘I ran home to get some towels, and we wrapped them up, took them home and called the RSPCA.
‘We were happy to keep them for the night and look after them, but they soon won us over, and we have decided to keep them ourselves.
‘We have only had them a few days, but their playful personalities are already coming out.’
Luke said the baby cats are now happy in their new home, where they love playing and cuddling.
He added: ‘They are really cute – I just don’t know how anyone could have done this to them – they would have suffocated slowly in that bag, and it was just a chance that we happened to find them.
‘I think it was fate that we walked that way and came across the kittens and that we were destined to keep them.
‘But I would like to help find the person responsible for such a sickening act of cruelty.’
Natalie Hill, an RSPCA inspector, is appealing for help to find whoever is responsible for this ‘callous’ act.
She believes the kittens were abandoned not long before Luke and Lauren found them at 7:30pm.
She said: ‘This is appalling and whoever is responsible must be callous to discard two kittens in a bag and throw them away like rubbish.
‘If it wasn’t for Luke and Lauren luckily finding them they would have suffered a lingering and terrifying death.
‘I am just hoping someone may have seen something suspicious and will help me with my investigation.
‘I am also appealing to see if anyone knows of anyone who had any kittens like these recently but are no longer in possession of them.’
Do you have a story to share?
Get in touch by emailing MetroLifestyleTeam@Metro.co.uk
MORE : Adorable kitten born without a bottom is now thriving after life-saving surgery
MORE : Disabled cat found abandoned as a kitten uses wheelchair to get around
MORE : Meet Shani, the would-be guide dog whose best friend is an 11-year-old girl with disabilities