The two heavy metal benches, which were bolted to the slabs on Blackford Hill, were torn up, dragged down the hill and dumped in bushes.
The vandals also smashed a computer at the site close to Blackford Pond, sending glass, electronics, wires and plastic into the pathway and grass area. Empty bottles of lager and cans of cider were strewn around the area.
The vandalism, which is believed to have happened some time between Tuesday and Wednesday, shocked visitors to the hill yesterday morning.
Ian Hudson, 60, who lives in the Grange, walks his dogs up Blackford Hill almost every day and regularly takes a breather at the beauty spot.
He said: "I quite often use the benches because it's a rendezvous point for the dogs. I was last up here on Monday and everything was fine. I have never seen anything like this before, it's horrendous.
"There's certainly no easy way of getting up here. Whoever did this has come up here carrying a computer with the intention of doing this."
Dawn MacBean, 37, has been carrying out work on Blackford Hill with the British Trust for Conservation Volunteers for the past couple of months.
She said she couldn't believe her eyes when she discovered the vandalism yesterday morning.
She said: "There's an odd case of litter up here but that's about the extent of it. Those benches are quite heavy so there must have been a few people doing it.
"To make the effort to come up here just to do that is disgusting. It's a lovely spot and now it's just a complete and utter mess."
Local councillors have also hit out at the vandals.
Newington councillor Fred Mackintosh said there was a problem with vandalism on the hill.
He said: "I'm not surprised about the vandalism because there is a little bit of a problem up there - but I am surprised that people have smashed things up.
"In January there were two deliberate fires started in gorse bushes."
Liz O'Malley, councillor for North Morningside/Grange said: "It's difficult to understand this kind of vandalism where people go to so much trouble to destroy something which gives pleasure to others.
"I hope the police are successful in tracking down the vandals."
Councillor Bob Cairns, the city's environment leader, said: "This is yet another disappointing example of mindless vandalism in our city's parks.
"It would have required some force and intent to smash the concrete plinths that the metal benches were bolted to.
"The benches are currently inaccessible as the area they are located in is wet and slippery.
"The benches themselves appear not to be damaged and if this is the case they will be reinstated as soon as possible."
A police spokeswoman said:
"It's a very destructive thing to do and we would ask anyone with information about this vandalism to contact the police."