After turning on the first system on Fakaofo, construction work would now begin on the second atoll.
Foreign Affairs Minister Murray McCully said turning on the first system was "a major milestone in the project".
When all three systems were fully operational by the end of the year, they would provide almost 100 per cent of Tokelau's power, he said.
"Many of our Pacific neighbours are reliant on expensive imported diesel for electricity generation and this is a barrier to developing their economies."
New Zealand was committed to supporting the roll-out of renewable energy technology in the New Zealand territory of Tokelau and the wider Pacific, he said.
The Tokelau Renewable Energy Project had been funded by The New Zealand Aid Programme and supported by the Government of Tokelau.
"New Zealand is advancing $7 million to Tokelau to fund installation of the systems," McCully said.
Bassett-Smith said there were issues across the Pacific with the financial and environmental costs of diesel-generated energy.
"Energy costs underpin the economic and social development of these nations."
Tokelau's diesel generators currently burned around 200 litres of fuel daily. About 2000 barrels were shipped in from New Zealand each year at a cost of NZ$1million.
Tokelauan government minister Foua Toloa said switching to solar would be a significant change from using fossil fuel and having to bring barrels to the atolls.
"It avoids expenses, but also bringing them there, it's dangerous and any spill will affect the environment."
Once work is complete, Tokelau would have replaced its diesel generators with 4032 solar panels, 392 inverters, and 1344 batteries weighing 250kg each.
The new solar power system would be able to survive cyclone force winds of 230 km/h.
Powersmart was recently ranked 14th in The New Zealand Herald's Green 50 list of top Kiwi companies helping the environment.
Tokelau has a combined land area of 10 km squared and its population of about 1400 currently have access to about 16 hours of electricity each day.
Powersmart's custom-designed solar system will provide 150 per cent of the nation's current electricity demand, the company said.
During periods of prolonged cloud cover, generators that run on coconut oil will supply power and simultaneously recharge the battery bank.
Powersmart has collaborated in the project with IT Power Australia.