Octopus bought the stake from AIP Management, the investment manager for Danish pension funds PKA and PFA, it said without providing financial details of the transaction.
Walney Extension is operated by Denmark's Orsted (ORSTED.CO), which holds a 50% stake. It has been operational since 2018, producing enough power for nearly 600,000 homes.
The latest investment was made through the 3 billion pound ($3.7 billion) Octopus Energy Offshore Wind fund the company launched this month.
Octopus Energy already holds stakes in British offshore wind farms Hornsea One and Lincs. It is also expanding its global investments in the technology globally with deals in Europe and Asia.