The New York Jets owner has bought the 43 per cent shareholding of fellow American John Textor.
An agreement was struck earlier this month and Palace confirmed last night the deal has now been formalised.
The purchase is said to be worth over £190m.
"I am honoured and privileged to be joining the ownership group of Crystal Palace Football Club," Johnson told the club's official website.
"It is an organisation with a proud history, tradition, and deep roots in English football in south London, which I came to admire during my time as US Ambassador to the United Kingdom.
"Eagles fans have demonstrated extraordinary loyalty, passion, and unwavering dedication and I am excited to meet and get to know them."
Palace chairman Steve Parish added: "We are delighted to be welcoming Woody to the ownership of the football club.
"We very much look forward to working alongside him to build on our historic recent success moving forwards."