Police said they were taken from Mr Venus' Morningside property between midnight and 6am last Wednesday.
One is from the English Championship League season 2007-08 for West Bromwich Albion while the other is from English Division 3 season 89-90 for Wolverhampton Wanderers FC.
Both medals are about 12mm in circumference and not in their presentation boxes.
A Lothian and Borders Police spokesperson said: "These items are of tremendous sentimental value, so I would appeal to anyone with any information to get in touch so we can reunite them with their owner.
"They are very unusual, distinctive pieces so I would ask people to stay alert if they are offered for sale."
As a player, Venus spent the majority of his career with Wolves and Ipswich. He is now the assistant boss at Middlesbrough alongside Tony Mowbray.