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.
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.
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.

13 July 2017 Last updated at 08:01 BST
She's now through to the semi final of the competition.
But this may not be an easy win as Konta faces five-time Wimbledon Champion Venus Williams,
Let's see how they stack up, stats wise.

Foreign investors have been blamed for driving up the cost of real estate in Toronto and Vancouver.
Hurt by failing oil prices, Canada's ailing economy has become a major issue as the country elects new leadership.
Mr Harper said that about 15% of condos in Vancouver aren't being lived in.
"If such foreign, non-resident buyers are artificially driving up the cost of real estate and Canadian families are shut out of the market, that is a matter we can and should do something about," said Mr Harper said, who was campaigning in Vancouver on Wednesday.
While home prices in the country's interior have fallen, prices have remained high in Toronto and Vancouver.
The average price of a detached home in Vancouver - the country's most expensive market - is more than $1 million (Â£640,000).
Harper's Conservative Party said it was looking into restrictions on foreign homeownership that have been put in place by other western countries.
Australia limits the ability of foreign buyers to purchase existing homes for investment, and only allow foreign investment resulting in new home construction.
If necessary, Mr Harper said the Conservative government will take action in coordination with the provinces to make sure foreign non-resident investment "supports the availability and affordability of homes for Canadians."
His administration also announced that Canadians will now be permitted to withdraw $35,000 (Â£17,241) instead of $25,000 (Â£12,315) from retirement accounts to purchase their first homes.

The girls were "touched inappropriately" in the Castaway Camp playground at the park in Windsor, Berkshire, on Thursday 11 August.
Thames Valley Police refused to give the suspect's age or say where he was arrested, citing "safeguarding issues".
The boy has since been released on police bail until 2 December.
Police previously issued an E-fit of a suspect, who was described as a white man in his teens or early twenties.
Officers said he was white, under 5ft 8in tall, wearing dark slim-fitting trousers, a dark t-shirt and trainers.
Police began following up new leads in September after a reconstruction was shown on BBC One's Crimewatch.
A 22-year-old man previously arrested on suspicion of carrying out the attacks was released without charge.
Thames Valley Police said: "This is remains a live investigation and we continue to appeal for the public's help".
Disused phone boxes in London are being put to a novel use - as solar-powered charging stations for mobile phones.
[NEXT_CONCEPT]
After an unbelievable year Johanna Konta is one of the favourites to win the Wimbledon 2017 ladies title.
[NEXT_CONCEPT]
Canadian Prime Minister Stephen Harper has announced plans to track foreign homeownership and raised the possibility of eventually enacting limits on buying.
[NEXT_CONCEPT]
A boy has been arrested in connection with the sexual assault of two six-year-old girls during a trip to Legoland.