Diamond Foods said its stockholders will get 0.775 Snyder's-Lance shares and $12.50 in cash for each share they hold.
The $40.46 per-share cash-and-stock offer represents a 16 percent premium to Diamond's Tuesday closing.
The deal is valued at $1.91 billion including $640 million of Diamond Foods' debt.
Kellogg was said to be in late-stage talks to buy Diamond Foods for more than $1.5 billion, the New York Post reported last week.
Oaktree Capital, Diamond's largest stockholder, has agreed to vote in favor of the transaction, Snyder's-Lance said.
Snyder's-Lance said the deal, which is expected to immediately add to its earnings, would expand its presence in the natural foods category.
Morgan Stanley is financial adviser to Snyder's-Lance and Troutman Sanders is the company's legal adviser.
Credit Suisse is financial adviser to Diamond and Fenwick & West is the company's legal adviser.