The pet was found outside Jasmil Kennels & Cattery in Upchurch, Sittingbourne.
A note accompanying the abandoned dog explained that his owner was leaving him after 10 years.
It read: "Please can you take me in as my owner has abandoned me after 10 years because I have not learnt to be good so I have been returned here where he found me.
"Thank you for looking after me, sorry for inconvenience."
Swale Borough Council stray dog service appealed for the owner to come forward in a message on its Facebook page.
"This elderly black Labrador was found tied up to railings at Jasmil Kennels this morning," read the statement.
"We would very much like to speak to the owner to establish why the dog was the dog has been abandoned. No chip.
"If you recognise him and can be of any assistance, please contact the council in confidence or message this page. He will now be taken into our care."
Corrina Shuttlewood, the owner of the kennels, said they had been inundated with calls from concerned locals about the dog after the appeal was shared.
She told the Evening Standard that finding dogs tied to their railings wasn't a regular occurrence.
"It was a lovely dog. He was happy to just stand there," said the kennels owner.
"It's not ideal to leave a dog tied to railings as you don't know how long they will be left there.
"Luckily we found him and I'm sure the local authority won't struggle to find him a new home."
It comes after a brindle and white Staffordshire bull terrier-cross was abandoned by its owner at a Blackpool church with a note saying "I love you and I'm so, so, so sorry".