Kirklees Council said the plan was to "target properties with poor thermal efficiency and households at risk of fuel poverty".
The solar panels will be installed on 50 homes this year, 1,000 next year and 950 in 2016/2017.
Councillor Cathy Scott said the authority expected the panels to reduce household bills by £100 each year.
"A reduction in fuel poverty is the key driver for the project rather than maximising income and the intention would be to target properties with poor thermal efficiency," she said.
The council hoped the project would be self-financing with "a future feed in tariff income of £14m overall based on the electricity generated".
It also expects 50% of the electricity generated by the solar panels to be used by tenants.
A £9.2m scheme for 2,000 solar panels to be installed on council houses in Kirklees has been given the go ahead.