A member of the public raised the alarm after finding the male dogs in Drumpellier Country Park, Coatbridge, tethered to a wooden fence.
A note was discovered beside the dogs which read: "Father went into a nursing home and we tried to rehome the dogs, but no luck.
"Desperate times led to this."
The pets - a black crossbreed which is three to five years old and a brindle Staffordshire bull terrier cross, thought to be around five to seven years old - were taken to Shettleston Police Station where they were later picked up by the SSPCA.
The pair were taken to the charity's Lanarkshire Rescue and Rehoming Centre in Hamilton where they have been named Finn and Xander.
Inspector Laura McIntyre said there is "no excuse" for abandoning an animal.
She added: "We are very keen to trace whoever has left Finn and Xander.
"The only clue we have is a note which was found beside the dogs indicating there may have been some problems which led to the pair being abandoned.
"We understand that it can be very difficult at times to care for pets due to changes in personal circumstances but there is no excuse for abandoning an animal.
"Both dogs were examined by a vet who found them to be underweight and we are reaching out for anyone with information to get in contact with us.
"Finn and Xander are both super friendly dogs and we will continue to care for them until we can find them loving new homes."
Abandoning an animal is an offence under the Animal Health and Welfare (Scotland) Act 2006 and anyone found guilty of doing so can expect to be banned from keeping animals for a fixed period or life.
Anyone who recognises Finn and Xander is being asked to call the SSPCA Animal Helpline on 03000 999 999.