Fyffes produces, ships, ripens and distributes bananas, melons, pineapples and mushrooms.
The firm, which has its headquarters in Dublin, employs more than 17,000 people worldwide and has an annual turnover of €1.2bn.
Sumitomo supplies about one in three bananas sold in Japan after first entering the market in the 1960s.
The Japanese company said it would pay €2.23 euro per share, representing a 49% premium on Fyffe's closing price on Thursday.
The Irish firm has recommended the deal to shareholders and said 27% had backed it.
David McCann, chairman of Fyffes, says: "We believe this transaction represents a compelling proposition for our shareholders and crystallises the substantial value created in recent years through the various strategic developments and the strong operating performance."
Sumitomo said it was drawn to Fyffes' "strong position" in complementary markets and promised to invest further in the business.
"We look forward to working with the Fyffes team to further develop the business over the longer-term and to expanding into new markets," said Hirohiko Imura, managing executive officer.
In September, Fyffes itself snapped up Canada's All Seasons Mushrooms in a €41m deal, its second such acquisition in six months.
It followed the takeover of Ontario-based importer Highline Produce in April.
Irish fruit distributor Fyffes has agreed to be bought by Japan's Sumitomo in a €751m ($798m; £634m) deal.