The thief made no attempt to hide his identity as he wandered round the shop before making off with more than 1,000.
Police are now hunting the man, believed to be aged around 30, after the break-in at around 4:45pm on Sunday at the shop in Niddrie Mains Road.
Owner Muzzamil Malik said the thief made off with two-and-half days' takings, as well as around 50 packets of cigarettes during the raid, which he loaded into a white bag.
The 31-year-old also believes the thief – who wore a woolly hat and hooded top – stole his baby daughter's portable DVD player, which had been left in the store.
Local residents are understood to have supplied police with the name of the suspect and officers today said they were "following a positive line of inquiry".
Mr Malik, who has owned the MVC Your Local Store for less than a year, said: "I had just locked my shop door from the inside. There were children playing outside the shop so there was a lot of noise. I never heard anything."
When Mr Malik re-emerged only a few minutes later, he saw that someone had forced open the front door and made off with cigarettes from behind his counter.
He said: "The man had broken the lock on my door to get in. I thought the till was locked up but CID officers who came to the shop later said there was an emergency button which can over-ride the lock and open the till. The thief must've known where that was.
"I had been to the bank on Friday afternoon so I had all my takings from the rest of Friday, Saturday and Sunday in there.
"I'm waiting for the police to catch this man as they have the CCTV images, fingerprints, everything. I've seen him walking around this area before."
Mr Malik, a married father of two, studied law at the University of Edinburgh before opening his own business after graduating.
He added: "This man spent a few minutes wandering around the store so I'm checking my inventory to see what else he may have taken.
"My daughter also had a portable DVD player here so she could watch things at the store after finishing at nursery. That is gone as well."
A police spokesman said: "Lothian and Borders can confirm they are investigating following a theft from a store in Niddrie Mains Road that happened around 4:30pm on Sunday, 24 January.
"We are currently following a positive line of inquiry."