Dancers are to be told to go no further than topless as part of a new code of conduct for club operators.
Contact between dancers and customers will also be banned, as will performances in private booths.
In order to enforce the rules, clubs are to be ordered to install CCTV, and there will be undercover checks by council inspectors.
Club operators today accused the council of hypocrisy for cracking down on them while turning a blind eye to sex for sale in saunas.
Peter Stringfellow, who has been looking to open a club in Edinburgh, said city councillors were being "immature, silly and hypocritical".
"Edinburgh has to decide whether it wants to license places like this or not," he said.
"If it does, then it can't go all moralistic about it and try to introduce silly rules like this."
Mr Stringfellow, who runs one of Britain's most famous strip bars, urged the council to copy rules laid down in Westminster, which allow nude dancing but no contact between dancers and patrons.
Unless the council changed its mind, he said, he would abandon plans to open a club in the city.
Gino Diponio, owner of the Fantasy Bar on Shandwick Place, said the move threatened to put the Capital's lapdancing clubs out of business.
He added: "I just can't see people coming here if dancers are not going to go completely naked.
"People expect that when they pay their money. It's like going to the pub for years and then finding it's stopped serving alcohol.
"We are more than happy to comply with any other rules, but this is ridiculous.
"We have 20 staff working here and all of their jobs will be at risk if this goes ahead. We won't be able to survive."
Mr Diponio said councillors were guilty of "hypocrisy" in trying to clamp down on nudity in lapdancing bars and clubs when they licensed saunas known to offer sex for sale.
The rules are the first to be introduced for Edinburgh's lapdancing clubs, many of which currently operate with a basic pub licence.
Clubs which break the rules face the threat of having their hours cut or losing their licence.
They will have to hand over CCTV tapes to council officials investigating any complaints.
Inspectors will also make unannounced visits to the clubs. The city's licensing board is expected to approve the code of conduct on Monday.
The rules are being brought in ahead of a Scottish Executive plan to introduce similar rules within the next three years. However, the Executive is expected to leave the question of whether full nudity should be allowed to local authorities to decide.
The move comes three years after Lothian and Borders Police raised concern about the growth of lapdancing bars and clubs in the city.
Police chiefs said it was a "loophole" in the law that allowed them to operate without strict supervision. They called for stricter rules on "no touching" between clients and dancers, the widespread use of CCTV in premises and designated licences for lapdancing premises.
Licensing leader Phil Attridge said: "We don't see any need at all for full nudity in these places, there's no justification for it. We have had a number of concerns from members of the public and from women working in these places about the kind of things that go on inside them and we think all these measures will help. The no-nudity rule is for the protection of the people who work there."
A spokesman for Lothian and Borders Police said: "We welcome any proactive moves taken by the legislators to regulate and protect the public and performers.
"It would put in place procedures and policies to make licensees more accountable, and in the interim, this is a positive move forward."
New rules for lapdancing bars and clubs
• No full nudity.
• Dancers should only perform in open public areas, which at all times should be stewarded and covered by CTTV. No dancing allowed in private booths.
• No touching between dancers and patrons at any time.
• Dancers should remain fully clothed when not performing.
• Any advertising of performances outwith the licensed premises may only depict dancers suitably clothed (i.e. not fully naked).
• Each licensed premises must have a full register of the dancers that perform there, including their names, ages and current addresses.
• Foreign nationals must provide a passport and licence holders must check they are entitled to work in the UK.
• All changing facilities should be secure, private and single sex, and should not be accessible to patrons.