Council workers Charles Owenson, 62, and James Costello, 44, received bribes from businessmen Kevin Balmer, 52, and Brendan Cantwell, 44.
The council employees helped award contracts to Edinburgh Action Building Contracts Ltd (ABC Ltd).
The charges related to the maintenance of council buildings from 2006 to 2010.
The four men, who had earlier pled guilty, were remanded in custody on Tuesday at Edinburgh Sheriff Court. They will be sentenced on Friday.
Sheriff Michael O'Grady QC told them: "Having regard to the gravity of the offences, it is clear to me the sentences will require to be custodial and require to be significant."
Balmer and Cantwell are former directors of ABC, which went into liquidation in 2010.
The court heard that Cantwell runs another company, Action Scaffolding, which continues to work for Edinburgh City Council legitimately.
The court heard that Owenson and Costello were provided with hospitality including corporate seats at Hibs and Hearts football grounds, meals out and visits to bars as well as cash.
The contractors even submitted inflated invoices to the local authority for work carried out to cover the costs of the bribes they were paying council officials.
Fiscal Keith O'Mahony earlier told the court: "In essence, the council was being charged for the cost of bribing its own officials."
Invoices were found that were falsely inflated to the value of more than Â£67,000.
The prosecutor said the hospitality the firm provided was "extensive" and added: "Drinks and lap dances were purchased for Owenson and Costello."
The pair also had expensive cars including an Audi TT Quattro and a Mercedes ML320.
Owenson and Costello allocated work orders to the firm valued at a total of almost Â£1.5m.
Four men who admitted corruption charges over Edinburgh council building repairs have been warned they face "significant" prison sentences.