The male dogs were found bound to a wooden fence in Drumpellier Country Park, in Coatbridge, North Lanarkshire, by a member of the public.
A handwritten note was discovered beside them, which read: "Father went into a nursing home and we tried to rehome the dogs, but no luck. Desperate times led to this."
The dogs, a black crossbreed around 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 and later picked up by the Scottish SPCA.
They were brought to the SPCA's Lanarkshire Rescue and Rehoming Centre in Hamilton on Friday where they have been named Finn and Xander.
SPCA Inspector Laura McIntyre said: "We are very keen to trace whoever has left Finn and Xander."