Two large, old-line brokerage houses announced today that they have agreed in principle to combine their operations, one of the largest mergers in Wall Street history.

The new firm-which would be a combination of Loeb Rhoades, Hornblower and Co. and Shearson Hayden Stone, Inc.-reportedly would become the second largest securities firm in the industry behind Merrill Lynch and Co. The firm would be renamed Shearson Loeb Rhoades, Inc.

Shearson said it would issue $90 million of its debt and equity securities to partners of Loeb Rhoades in exchange for its business. The merger will require approval of the Justice Department and the new stock issue by Shearson would require approval of its shareholders.

Shearson is a publicly held company whose stock is traded on the New York Stock Exchange while Loeb Rhoades is privately owned.

Sanford I. Weill, Shearson chairman, will be chairman of the new firm, while Sherman R. Lewis Jr., one of the three co-chief executives at Loeb Rhoades, will become president of the combined brokerage house.

According to the firms, when the two firms are consolidated, all processing of accounts will be done on Shearson's system.

Loeb Rhoades, which combined with Hornblower, Weeks, Noyes and Trask Inc. a year ago January, has had serve backroom problems ever since the merger, holding down its earnings at a time when most Wall Street houses were reporting high profits because of big trading volume in 1978.

The company lost money during the final three months of 1978.

During the first nine months of its current fiscal year (which ends June 30) Shearson earned $13.9 million, compared with $10 million for the full 12 months which ended June 30, 1978.

Shearson has 130 domestic branch offices and 14 foreign branches, while Loeb Rhoades has 150 domestic offices and 11 foreign branches. Presumably many of the branches will be consolidated as will some of the sales force.

The combined firm will have one of the largest investment banking operations on Wall Street as well as one of the largest commodities operations.