The appointment of CCB follows a memorandum of understanding between the Bank of England and the People's Bank of China signed on March 31.
CCB - one of the big four banks in the world's second biggest economy - opened its office in the capital in 2009.
The Government said the move - part of plans to strengthen the City as a western hub for Chinese finance - boosted the capital's position as a centre of RMB trading.
Two thirds of all RMB payments outside China and Hong Kong already take place in London, the Treasury said.
The capital dominates the 5 trillion US dollars (£3 trillion) a day global foreign exchange market.
The Treasury said the appointment would "give the UK's global financial services sector the confidence and infrastructure it needs to expand their RMB activities".
It will complement the existing clearing and settlement infrastructure for RMB trading in Hong Kong and "ease the transfer of funds in the western time zone", the department said.
Bank of England governor Mark Carney said it was "another important milestone on the progress towards greater cross-border use of the RMB".
"As the official clearing bank, China Construction Bank will play a valuable role in facilitating greater use of the RMB for trade, investment and other economic activities in the UK, particularly by providing a further option for UK firms to clear and settle their RMB activity within the London market," Mr Carney said.