During the risk of closure in 2023 Capital Theatres, which also run the Festival Theatre and Studio Theatre, were £8.9m short after they were hit by soaring costs driven by inflation.
The charity raised £26m to support the theatre.
This was then topped up with an extra £3m from the council and an additional £3.85m pledged by the Scottish government.
Work has been taking place since then but is nearing completion ahead of the summer opening – in time for the Edinburgh International Festival 2026.
Staff at the theatre described the final stages of the refurbishment as exciting and confirmed there would be celebrations held for the reopening.
A Capital Theatres spokesperson said: “As construction continues, attention will soon turn to the final decorative details that will bring all these spaces together.
“Each week brings the King’s one step closer to reopening, and we look forward to sharing more updates as the project reaches the finish line.”