Former Federal Reserve Board Chairman Arthur F. Burns accepted yesterday a $50,000 post at the American Enterprise Institute as a full-time distinguished scholar in residence. He also will teach an undergraduate seminar at Georgetown University this fall, where he will have the title of distinguished professional lecturer.

Burns chose the post with the conservative American Enterprise Institute, it was learned, over an offer from the Brookings Institution, another research organization in Washington generally considered to have a liberal orientation. He will have a staff of assistants, AEI said, and be free to pursue subjects of his own choice.

Burns is known to have received numerous offers from universities, business corporations and publications to teach, advise or write. Both he and Mrs. Burns were anxious to remain in Washington.

AEI officials said that Burns would hold a press conference Monday morning to discuss his new role, and to comment on the current economic situation.

In his final public statements before leaving the Fed, Burns had urged President Carter to be more forceful in protecting the value of the dollar, and to mount a more vigorous anti-inflation program. He has been speaking on these same subjects in a recent lecture series in Japan and Australia.

Burns, 73, retired as a member of the Fed on March 31 after being passed over by President Carter for reappointment as chairman, a post he had held for eight years. He was succeeded by G. William Miller.

He is considered to be perhaps the world's most renowned student of the business cycle, a subject - among others - he will continue to explore at AEI. In his role at the Fed, he became one of the most powerful influences in shaping the U.S. economy. His views were widely sought in Congress and in international financial circles.

AEI in recent years has been enhancing its reputation for scholarly research, offering an alternative, from a conservative point of view to Brookings. Burns' new AEI title puts him at the top of about 30 scholars and program directors including former President Ford, who is the distinguished fellow and economists Gottfried Haberler and William J. Fellner who are resident scholars.

Burns' seminar Georgetown will be for undergraduates and is titled: "Economic Policy in Relation to the Business World." University officials would not disclose Burns' salary, but said it was an indefinite appointment to the staff.