Ally Pally, as it is known, is where the first BBC television broadcast was made. The lottery-backed refurbishment will make it a TV-themed visitor centre, designed by architect Feilden Clegg Bradley Studios.
The Heritage Lottery Fund is contributing nearly £19m, and the London Borough of Haringey nearly £7m, towards the £27m project. However, Alexandra Park and Palace Charitable Trust still needs to raise the final £1m before work can start.
"Many of our team grew up enjoying the delights of Alexandra Palace,” said Chris Tredget, managing director of Willmott Dixon in north London. "So we’re delighted to have a lead role in shaping its exciting future as North London’s most iconic building."
Alexandra Park and Palace chief executive Louise Stewart said: "Almost half of Alexandra Palace is still inaccessible to the public. This project will help put that right. "When we're finished, Alexandra Palace’s eclectic history will finally come alive. It will be about Britain's innovators and pioneers, about cinema, comedy, opera, plays - a true family day out - as well as the music, award-winning parkland, views and ice skating we're famous for today."
Willmott Dixon's initial works include protecting the East Wing's historic features, stripping out dilapidated modern fittings and removing asbestos, which was used throughout the East Wing for sound-proofing and fire-proofing.