The company has taken two years to get to the point of getting the green light from Transport for London (TfL), but has now been allowed to go ahead with the scheme, chief executive of the company, Richard Corbett, confirmed in a blog post last week.
Users of the service will get 15 minutes of free "high-speed" Wi-Fi access after sitting through a 15-second video advertisement.
"This is really great news for London. With dwell times averaging 15 minutes in the back of a taxi, what better way to pass the time than to use your laptop, tablet, book reader or phone with guilt-free internet access," Corbett said.
"Tourists and business travellers can now access their emails, talk on Skype or surf the web without the fear of being hit with high data roaming charges when they return home," he added.
The company said it is already in "progressed conversations" with major consumer brands that include a credit-card company and a mobile manufacturer to sponsor the rollout of the service in "early 2013".