Anthony H. Griffin, Arlington's deputy county manager, will become the new city manager of Falls Church, succeeding Harry E. Wells, who has run Virginia's smallest city for 20 years, the city announced yesterday.

Griffin, 36, is expected to move into the new $2 million wing of City Hall soon after it opens in mid October. His appointment to the $52,500 post is scheduled to be approved by the City Council Aug. 29.

At a press conference yesterday, Griffin called Falls Church a "sophisticated city," despite its population of less than 10,000, with the same urban problems he has had to face daily in nearby Arlington: highway and commuter traffic problems, old shopping centers that need upgrading and housing problems.

He said that if he has a managerial style it probably would be described as "management by walking around. I like to get out and see what people are doing.

"I have high standards, but I'm not a drill sergeant," said the former U.S. Marines captain who served in Vietnam. A 1968 graduate of Yorktown High School in Arlington, Griffin attended Hobart College in Geneva, N.Y., and holds a master's degree in urban and regional planning from Virginia Tech. He has worked in the Arlington city manager's office since 1975, and his present salary is $49,500. Wells is currently paid $52,000 a year.

Griffin, his wife and two young children are expected to move into the city by next summer, a stipulation of the job, Mayor Carol W. DeLong said yesterday at the press conference.

Griffin was selected after an intensive three-month search by City Council members, who recently narrowed the candidates to four from Virginia and four from out of state, DeLong said. But, she said, "the candidates in Virginia had an advantage, especially those working in a metropolitan area."

Wells, who recently turned 66, took no part in the choice of his successor but did take the candidates on tours of the city. He said after the press conference that he was very pleased with the council appointment.

Wells said that after working for the city for 35 years, starting as a $67-a-week town clerk, "I'm ready to drop out of sight . . . for a year at least . . . and travel.

" . . . I don't think I'll ever attend another night meeting. Some 35 years of night meetings is enough."