The City of Edinburgh Council has been planning to build a new school on the park to replace the current 1960s tower block, which houses Portobello High School.
The project was given the all-clear by the city council four years ago.
But campaigners delayed the signing of a contract with Balfour Beatty after launching legal action claiming the council had no right to build the new school on common land in the city.
A Court of Session ruling that the site is “inalienable common good land” stalled the proposals even further.
This forced the local authority to submit a private bill to the Scottish Parliament last year to change the use of the park.
After being approved by MSPs in June, the bill was given Royal Assent on Friday and came into force this week.
Cllr Paul Godzik said: “Now that Royal Assent has been received, it will be full steam ahead with our plans to replace Portobello High School.
“Over the last few weeks, since the parliament approved the legislation, officers have been preparing to appropriate the park and sign the building contract with Balfour Beatty and both will now take place over the next few days.”
The scheme has been designed by JM Architects and Parsons Brinkerhoff structural engineers.
It will accommodate 1,400 pupils and feature a 25m swimming pool and sports pitches for community use.
Existing Portobello High School will be demolished
Balfour will build the new school on green belt land