The transaction, expected to be completed after the summer, will have to be approved by shareholders, reports BBC.co.uk.
The firm manufactures inverters, which transform the direct current produced by solar cells into the alternating current required by electricity grids.
According to ABB, demand for inverters is expected to increase by 10% a year until 2021, due to growing demand for energy, and rise in electricity prices.
ABB’s offer price of $6.35 per share represents a 57% premium over Power-One’s closing price per share on Friday at Nasdaq.
The California company generated a profit of $120m in fiscal 2012.
With the cost of solar energy drastically dropping, it expected to be cheaper than other sources of energy on national electricity grids by 2021.
Power-One has over 3,000 employees across its units in China, Italy, the US and Slovakia.
