Hill & Knowlton, Washington's largest public affairs lobbying firm, said yesterday it will acquire a lobbying firm headed by Craig L. Fuller, once the top aide to former vice president Bush.

The acquisition will join two of the most politically well-connected public affairs firms in Washington, and ends what apparently was a scramble by other public relations companies to buy Fuller's company, Wexler, Reynolds, Fuller, Harrison & Schule. Terms of the deal were not disclosed.

The Wexler firm will be operated as a separate unit, to be called the Wexler Group, with all of its 34 employees joining the 210-member Hill & Knowlton D.C. staff.

Fuller, 39, will be named president and chief operating officer of Hill & Knowlton Public Affairs, reporting to Robert K. Gray, the chairman and chief executive of the company's worldwide public affairs division.

Both Fuller and Gray indicated yesterday that Fuller is the heir apparent to succeed Gray, 67, who was closely associated with the Reagan White House and often is considered Washington's preeminent lobbyist and public affairs consultant. However, Gray said he has no immediate plans to retire.

Fuller was Bush's vice presidential chief of staff and previously worked for the lobbying firm headed by former Reagan aide Michael Deaver. In addition to Fuller, the firm's partners include Anne Wexler, a former assistant to President Jimmy Carter, and Nancy Clark Reynolds, who is prominent in Republican circles. Its clients include American Airlines and MCI Communications Corp.

Hill & Knowlton's Washington office includes Frank Mankiewicz, the press spokesman for George McGovern's 1972 presidential campaign, and Gary Hymel, who was chief of staff to Thomas P. "Tip" O'Neill in the House speaker's office. Hill & Knowlton, owned by the British communications company WPP Group, has done work for dozens of Fortune 500 companies and foreign governments.

Fuller said other firms expressed interest in buying his firm during negotiations with Hill & Knowlton. Sources said the interested parties included Shandwick PLC, the British company that topped Hill & Knowlton last year in fee income to become the world's largest public relations firm.