Tokyo Electron CEO Tetsuro Higashi added, "I think this combination will succeed very much."
Santa Clara-based Applied's stock rose $1.45, or about 9 percent, to close at $17.44.
Under the deal, which the companies hope to complete as early as the middle of next year, Applied's stockholders would own 68 percent of the as-yet-unnamed new company and receive one share in the venture for each Applied share they hold. Tokyo Electron shareholders would get 3.25 shares for every share they hold of the Japanese company.
The merged business would be headquartered both in Santa Clara and Tokyo, listed on both the Nasdaq and Tokyo Stock Exchange, and overseen by a board made up of five members from each corporation, with another board member to be mutually agreed upon by the two firms.
Higashi will be its chairman and Dickerson, who recently replaced Michael Splinter as Applied's chief executive, said he will move to Tokyo to oversee the integration of the two businesses.
The companies said their combination will produce a powerhouse with a stock market value of $29 billion. Applied employs about 15,000 people worldwide and its sales for the past 12 months totaled $7.2 billion, while Tokyo Electron employs about 12,000 people and had sales of $5.4 billion.
Randhir Thakur, an Applied executive vice president, said the merger "could include cost savings and adjustments," but added, "as far as layoffs, it's too early to say anything about that."
He said Applied has about 8,000 Bay Area workers.
The semiconductor equipment business has been sluggish lately, due partly to the decline in sales of chips for personal computers, which consumers are shunning in favor of smartphones and tablets. That has hurt Applied's business. In its most recent quarterly financial report, its profit tumbled 23 percent to $168 million compared with the same period a year ago and its sales of $1.98 billion were down nearly 6 percent.
Both companies took pains to note that they will function as equals in the merger. The new business will be incorporated in the Netherlands, a site chosen because both firms considered it neutral territory.
The purchase is the largest of a Japanese company from outside the country since Citigroup's $8 billion deal for a majority stake in Nikko Cordial in 2007, according to data compiled by Bloomberg.