Apptitude Media promises to "help-reinvent the magazine, combining old-world publishing expertise with a proven talent for publishing to tablets and smartphones", the new company said in a release.
It will focus on further developing the BJP's iPad and iPhone editions, and will launch a new iPad-only title called Fade to Black, which is being developed by the BJP team.
The buyout also sees Apptitude acquire Popular Science UK from Incisive, an iPad-only title which is a spin off of the US magazine, and 125, a twice yearly print title and iPad app focusing on photography, fashion, art and visual culture.
The management buyout has been led by Marc Hartog, founder and chief executive of the new digital media company, and the team behind the magazine remains the same. Incisive takes a minority stake in the new enterprise.
The buyout "gives us breathing room to be agile in a way that it's hard to be in a big publishing company that's focussed on business", explained Tom Royal, formerly tablet development manager at Incisive and now chief technology officer of Apptitude Media and also editor of Popular Science UK.
The team will have "more freedom and more speed", he added.
The print edition of the BJP, which launched in 1854, was re-launched by Incisive. Two years ago a team was assembled to work on a quarterly iPad edition, which was released in late 2011. "We cautiously hoped for 5,000 downloads in a year, and we were blown away by the response," Royal told Journalism.co.uk. "We beat our expectations for the year in two days."We cautiously hoped for 5,000 downloads in a year, and we were blown away by the response. We beat our expectations for the year in two daysTom Royal
The photography title has now been downloaded 200,000 times and has won an award, he said.
"It was a huge success for us," Royal said, explaining that led the BJP team to bring out an iPhone edition. "We have gone for something different with iPhone," Royal said, adding that the team did not simply want to "squish" the magazine down to the smaller screen size.
Both iOS editions use Mag+ technology. In a release from Mag+, Gregg Hano, the company's chief executive, said: "In my opinion the team are doing some of the best work in the digital publishing space, among the top 1 per cent of digital publishers in the world."
"The iPad allows you to do new things," Royal added, explaining that the niche magazine, which focuses on cutting edge photography, including art and fashion, is expensive to produce in print.
Based in Soho, Apptitude Media describes itself as is a new digital media company "with a portfolio that includes some of the most successful and revolutionary digital magazines in the industry."