British Land and Oxford Properties have exchanged contracts for the sale of the Leadenhall Building to C C Land for £1.15bn.
Shareholders of the Hong Kong-listed C C Land must now approve the sale before it can be completed.
Tim Roberts, head of offices and residential, British Land, said: "British Land and Oxford Properties took a bold step at the early stages of the UK's economic recovery to develop the Leadenhall Building to generate a high quality, long term income stream.
"It's a decision which has really paid off. Through a strong, collaborative partnership, we have delivered an iconic, award-winning building let to high calibre occupiers at record City rents."
Yesterday, it emerged that British Land was looking for a buyer, and that it was aiming for £1bn, but the company said it was not sure the on-going discussions would lead to a deal.
Construction of the Cheesegrater started in 2011, and it was completed in 2014. The 46-storey building became fully let in July last year, with the remaining floors going to Kames Capital, MS Amlin and Rothesay Life.
C C Land shareholders will vote on the deal at a special general meeting and must approve of it on or before 28 June in order for it to go ahead.
Property mogul Cheung Chung Kiu controls 50.4 per cent of the shares in C C Land through his companies Fame Seeker Holdings Limited and Thrivetrade Limited. It is thought he will be voting in favour of the purchase, in which case completion will take place five working days later.