NHS Lothian had said it hoped the facilities, which will provide 31 extra beds at the Royal Infirmary of Edinburgh, would be opened by the summer and provide extra capacity over the busy winter period.
But the project was hit by delays due to contractual wrangles with Consort, the private firm which owns and runs the hospital under a Private Finance Initiative deal.
The health board was eventually forced to agree to a clause that meant it would be unable to impose penalty points under the terms of the contract if there were later issues with the building work that was needed to transform office space into patient areas.
Jim Eadie, SNP MSP for Edinburgh Southern, accused the hospital owner of "attempting to hold NHS Lothian to ransom" after details of the negotiations were made public.
The new areas will be used to treat orthopaedic patients.
Lyn McDonald, Royal Infirmary hospital director, said: "The staff have been fantastic during the construction process and have proved vital in informing the development with their own experiences, skills and expertise.
"Clearly there will be a huge benefit to patients and having these new wards will allow us to improve the patient experience on the site."
Health Secretary Alex Neil has repeatedly stated that the capital's Royal Infirmary was 20% too small when it opened in 2003.