MORRISTOWN, N.J. (AP) _ The chairman of Allied Corp. said the company's merger with The Signal Cos. Inc. of California, which will create a $13.5 billion aerospace and chemical firm, was a ''once-in-a-lifetime'' chance to build an ideal company.

''In a single stroke, we will add massive new strength to our core businesses,'' said Edward L. Hennessy Jr., following Wednesday's vote by Allied Corp.'s stockholders.

Hennessy profusely praised the merger, which was approved later in the day by Signal's shareholders. He called the acquisition ''probably one of the largest non-oil company mergers in United States history,'' and added that the new Allied-Signal Inc., based here, will be a ''world leader'' in the aerospace, automotive and chemical industries.

The merger is ''a once-in-a-lifetime opportunity to build this ideal company,'' said Hennessy, who will chair the new corporation.

The enlarged company will total 168,000 employees and have liquid capital of $1.4 billion. Hennessy said much of the cash will be used to call in outstanding stock, and build the company's debt capacity - increasing its ability to grow even further.

Hennessy also said, however, that some staff cuts will be likely after the merger.

''If there is any reduction in jobs as a reult of the restructuring, we will manage it primarily with such methods as attrition and early retirement incentives,'' he said.

Shareholders voted overwhelmingly for the merger at a special session called to approve the deal announced in May. Signal's shareholders approved the merger Wednesday afternoon in San Diego, Calif.

More than 116 million Signal shares, or 86.6 percent, were voted in favor of the merger while 1.5 million shares were voted against. An estimated 250 shareholders at the special session represented 97.9 percent of the company's outstanding shares.

''In the long haul, the tools are there to create a significant earnings increase,'' Signal chairman Forrest M. Shumway said. ''If we didn't think so, we wouldn't be making this deal. A big reason for making this deal is because we think the futures are there. Signal shareholders are coming off very well.''

About 61,000 Allied shareholders, or more than 82 percent, voted in favor of the merger, and nearly 3.7 percent, or about 2,700 shareholders, voted against. The others did not cast a vote.

The cash and securities merger is valued at between $4.5 billion and $4.9 billion.

Based on 1984 results, the combined company would have revenue of $16.7 billion, earnings of $773 million and assets of about $13.5 billion, Hennessy has said.

Allied brings to the deal its traditional mainstays, synthetic fibers and industrial chemicals, along with holdings in aerospace, oil and gas and other technologies.

The corporation of more than 114,000 employees had income of $487 million in 1984. The corporation, based here, has several wholly owned subsidiaries, including the Bendix Corp.

Signal, based in La Jolla, Calif., has 54,000 employees and took in $285 million in 1984.

The company's chief strength is in the aerospace, electronics and instrumentation fields, focusing on advanced technology.

Signal's Garrett Corp. manufactures jet engines for commercial and military aircraft. The Ampex Corp. subsidiary is a leader in electronics and recording technology.

Hennessy said combination of the companies may result in a reduction in employees. But he vowed the cuts would be handled by attrition and early retirement incentives.

Under terms of the merger, top Allied officials are scheduled to receive a total of $15 million and Signal's chief executives will get $26 million. Outside reports have put the total package for veterans of both companies as high as $50 million.

Officials said Hennessy, who is paid more than $1 million a year, will receive compensation totalling about $3.9 million in the next five years. Signal's top two officers, Chairman Forrest N. Shumway and President Michael D. Dingman, will share $7 million in benefits.