In an agreement that would create the largest bank in Virginia, with assets of almost $7 billion, shareholders of Virginia National Bankshares Inc. and First & Merchants Corp. yesterday approved a merger that would join the two holding companies.

In separate meetings, shareholders who control more than 75 percent of the stock in both companies voted for the merger, which has been under consideration since last December. The merger will become final at the end of 1983, subject to federal approval.

Under the agreement, First & Merchants Bank, Virginia's fifth largest bank, and Virginia National Bank, the state's second largest, would join to form Sovran Bank, which would have 37 branch banks in the Washington area. The joint holding company would become Sovran Financial Corp.

The name Sovran was chosen because it is the "poetic" spelling of sovereign, an old English gold coin, said C. Coleman McGehee, chairman of F&M.

With its combined assets, Sovran Financial would become the largest bank holding company in the Middle Atlantic States while Sovran Bank would rank in the top 40 banks in the country. Currently, Maryland National Corp. of Baltimore is the biggest banking operation in the region, with assets exceeding $4 million.

VNB shareholders would aquire 52 percent of the new holding company while F&M shareholders would obtain 48 percent. Under these terms, each outstanding share of VNB stock will be exchanged for 1.15 shares of common stock of Sovran Financial and F&M outstanding convertible stock will be exchanged for an equal number of shares of convertible stock in Sovran.

The impending deregulation of the banking industry spurred the agreement, which would be the largest in the state's history. It also is the latest in a series of mergers due to changes in Viriginia law that opened the way to bank consolidations.

The combination of the two banks into Sovran would represent "more viable competition when the day of interstate banking does come, and we don't think that day is too far away," McGehee said.

"The crux of the matter is banking is changing," said C. A. Cutchins III, chairman of the board of VNB. "You have to have a critical mass and strong capital to compete as a regional bank."

Cutchins will become chairman of the board and CEO for Sovran Financial Corp. and McGehee will become president, chief operating officer and chairman of the executive committees of both institutions.

The banks' operations complement each other, because their strengths lie in different areas, Cutchins said. They also are concentrated in different regions of the state, with VNB headquartered in Norfolk and F&M based in Richmond.

"Our managment philosphies are similar, something very important in any merger," Cutchins said. F&M's middle- to large-market corporate loans and trust division complements VNB's leadership in the development of electronic banking and emphasis on small business and customer service, he said.

The merger would prove "very advantageous" to Virginia, McGehee said, but he and Cutchins both said they did not expect it to affect the competition among the other banks in the state.

The merger evolved from a conversation between McGehee and Cutchins late last year, they said.