The commitment from John Studzinski – a Tate trustee – is the first major private donation towards the extension project and the largest individual gift ever made to Tate Modern.
The Transforming Tate Modern scheme – which received planning permission in March – will add a new building on the south-west corner of the site.
"I am delighted with the Transforming Tate Modern concept and this donation will allow me to fundraise for Tate with event more conviction than in the past," says John Studzinski.
"Tate Modern has been an extraordinary success under Nicholas Serota's vision and leadership and has a great track record. I believe in backing winners."
Tate director Sir Nicholas Serota described the donation as "a magnificent act of faith in a project that will transform the building and provide improved facilities for the next generation of visitors".
The gallery will spend the next 18 months raising further funds for the £165 million (£215 million at 2012 prices) scheme. If targets are reached construction work could begin in 2009 with completion in time for the London Olympics in 2012.
The Collection Centre proposal is likely to be brought forward in partnership with the National Portrait Gallery and other arts institutions.
If the project gains government backing this year the project could commence in 2009.
Next week 150 young people from across England will spend the night in the Turbine Hall at Tate Modern in tents they will decorate themselves taking their inspiration from works in the Tate Collection.
The event, which includes a consultation exercise to find out what young people want from Tate Modern's new building and a tour of the disused oil tanks beneath the current lawn, is part of Next Generation Tate, a new nationwide youth programme.
For Tate Modern this strategy aims to consolidate its reputation and turn the gallery into "a place of cultural and social interchange" to "energise the nation" through moderal visual culture.
In the autumn Tate will announce its plans for the Cultural Olympiad.