At 1000 feet (305m) high, it will be the City of London's tallest skyscraper and about 1m shorter than the Shard, Britain's highest building.
It will feature internal slides and moving transparent pods running outside the building for visitors to ride in.
The tower will be just a visitor attraction without any office space.
Around 20,000 free visits for state school children will be offered each year.
The viewing tower would be competing against similar paying attractions in the area offered by The Shard and the London Eye.
Foster + Partners, the architects which have designed the flower-like building, say they want it to complement the Gherkin next door which the firm also designed. The 590ft (180m) tower is officially known as 30 St Mary Axe, its street address.
The company's founder and executive chair Norman Foster claimed the Tulip would be a "cultural and social landmark".
Jacob J Safra, whose Bury Street Properties company is funding the project, added: "The Tulip's elegance and soft strength complements the iconic Gherkin."
If planning permission for the unusually-shaped building is permitted, the companies say construction would begin in 2020 with the project completed by 2025.