Roche said it aimed to buy up to 56.3 per cent of the US company, paying shareholders USD 50 per share, or a total of USD 780 million.
In addition, the Swiss group said in a statement it planned to buy five million newly issued FMI shares, for a total of USD 250 million.
Roche hailed FMI's "pioneering approach to genomics and molecular information", saying the deal would allow it to provide faster cancer identification and better personalised treatment.
As part of the deal, Roche has agreed to spend around USD 150 million funding FMI's cancer research and development efforts for at least five years.
The FMI board has already unanimously approved the deal, Roche said, adding that it expected the agreement to be finalised during the second quarter this year.