Under the deal, announced in November last year, BP bought the remaining 50.03% stake in LSBP from its founders and management.
BP said the buyout was closed for a total consideration of 400 million pounds ($518.00 million), with the addition of 2.1 billion pounds in debt.
The buyout underpins BP's drive to build up its low-carbon and biofuels production as part of its energy transition strategy.
BP added that the London-based solar developer will retain its standalone operating model and independent brand.
The London-listed oil company had previously said it will bring in a new investor in LSBP once the deal is completed.
Lightsource BP is now led by BP's Joaquin Oliveira and founder Nick Boyle as co-CEOs.