Francis M. (Bud) Mullen Jr. will announce today that he is resigning as head of the federal Drug Enforcement Administration, effective March 1, according to sources.

They said Mullen had informed FBI Director William H. Webster, Attorney General William French Smith and White House counsel Fred F. Fielding of his decision and will send a formal letter of resignation to President Reagan today.

Mullen has been largely responsible for the success of recent cooperation in drug-enforcement programs between his agency and the Federal Bureau of Investigation.

Federal sources said John C. Lawn, DEA's deputy administrator, is likely to be nominated to succeed Mullen if the Reagan administration decides to choose a career law-enforcement agent for the job, rather than a political appointee.

Three weeks ago, Mullen celebrated his 50th birthday, the retirement-eligibility age for federal law-enforcement agents.

Mullen was persuaded by Webster in 1981 to leave his job as executive assistant director for investigations at the FBI in order to head DEA and coordinate the new plan for shared responsibility between the two agencies on drug-enforcement cases. Mullen had been with the FBI since 1962.

Some DEA agents opposed the cooperative effort with the FBI, fearing they would be overshadowed by that larger and more powerful agency. But Mullen overcame much of that opposition and arranged compromises so that the FBI, with its larger numbers of agents and their specialized training, has been able to help the DEA on such matters as wiretaps and financial investigations.

Mullen had a difficult Senate confirmation process because of congressional criticism of his handling of the Abscam investigation and an FBI background check of Labor Secretary Raymond J. Donovan. Mullen was confirmed by the Senate on Oct. 7, 1983.

The sources said Mullen decided to leave his government job now because of two attractive private-sector job offers. The sources said Mullen also is considering running for public office, but he reportedly has not decided whether to run in his home state of Connecticut or in Virginia, his legal residence.