Tate Modern is a significant step closer to raising the £215m it needs for its extension after the Israeli shipping billionaire Eyal Ofer donated £10m.

The gallery gave the details of one of its biggest cash gifts on Tuesday. In recognition of Ofer's contribution, Tate Modern will name the level 3 east galleries the Eyal Ofer galleries.

The donation means its extension fundraising is almost there, with 85% of the capital-cost money raised for a project that will increase the gallery's space by 60%, and whch is due to open in 2015 or 2016.

The Ofer family is known for philanthropy. Eyal's late father, Sammy Ofer, was a major donor to the National Maritime Museum in Greenwich and the Cutty Sark restoration project.

The Tate's director, Sir Nicholas Serota, said: "I am delighted that the Eyal Ofer Family Foundation has chosen to make such a major contribution towards Tate Modern's future. It is exciting to see such outstanding philanthropy continuing from one generation to the next. The generosity of Eyal Ofer and his family will help to make Tate Modern a truly 21st-century museum."

Ofer said: "Tate Modern is one of the world's great public art institutions. So it is my privilege to be supporting this development project as it expands the gallery's exhibition space and enables an iconic institution to enhance the experience and accessibility of contemporary art for an even broader range of visitors from across the UK and abroad."