The exchange said it had agreed to buy the holdings of several, as yet, unnamed shareholders, for up to a maximum of 6.8 per cent of LCH's share capital.
The LSE added that all shareholders have been notified of the share sale in the update, made after the market's close.
It said confirmation of the LSE's total shareholding in LCH as a result of the acquisition will be announced "in due course". Up until this announcement, its shareholding was 57.8 per cent, which it has held since taking control of LCH back in 2013.
Last month, pan-European exchange Euronext agreed to swap its 2.3 per cent stake in the LSE's LCH Group for an 11.1 per cent shareholding in its French clearing arm, LCH SA.
“This transaction will strengthen the long-standing relationship between Euronext and LCH SA, and cement the strategic future of LCH SA,” Euronext said.
The tie-up came nearly six months after Euronext's deal to buy LCH SA in its entirety hit the buffers. The deal was dependent on the completion of the LSE's failed merger with Deutsche Boerse.
LCH has been in the spotlight since the Brexit referendum, as it is the main venue for processing euro-denominated swaps, but will no longer be within the European Union when the UK leaves in March 2019.