The first of six boxes was unveiled on Tottenham Court Road this week.
The service is free to use although users will be shown adverts as they wait for their phone to charge.
Many of the UK's red telephone boxes have largely fallen into disuse although some are being revived as libraries or being fitted with medical equipment.
The boxes have had a makeover for the project - painted green and fitted with a roof-mounted 86cm solar panel.
Inside there are a variety of charging stations for different models of phone and a screen which shows adverts.Battery life
The advertising screen is reinforced to deter vandals and the boxes are maintained daily and locked overnight.
The project was the brainchild of two geography students turned entrepreneurs Harold Craston and Kirsty Kenny.
Both studied at the London School of Economics (LSE) and were interested in finding new ways to use public spaces.
"I lived next to a phone box in my second year at uni and walked past it every day. I thought, 'There are 8,000 of these lying unused in London and we must be able to find a use for them,'" explained Mr Craston.
The solarbox can charge up to 100 phones a day, offering a 20% battery boost in 10 minutes.
Since launch, about six people per hour use the booth, according to the founder.
Running out of battery is a perennial problem for smartphone users as they become ever more powerful without an equivalent technology leap in battery life.
"On launch day, my phone ran out of battery and I genuinely had to use the box," said Mr Craston.Exclusive content The rise of smartphones has meant many telephone boxes have fallen into disuse
Solarbox won second place in the Mayor of London's Low Carbon Entrepreneur of the Year Award earlier this year and also won the LSE's Emerging Entrepreneur of the Year award.
Five more boxes will be rolled out by April 2015.
Funded by advertising, the founders are keen to make sure users are engaged by "short, fun and exciting ads showing exclusive content".
Firms signed up include Tinder and Uber, and 30% of advertising space is reserved for community projects.