Lee P. Brown, the public safety director who led the investigation into the slayings of 28 black youths in Atlanta, yesterday was named chief of Houston's troubled police department.

"They made him an offer he did not feel as though he could refuse," Atlanta Mayor Andrew Young said. "Houston is notorious for its big money offers. This was Lee Brown's decision on his own."

Brown, 44, who holds a doctorate in criminology, will earn $75,000 annually in Houston. He earned $41,423 in Atlanta.

"I had done a nationwide search, and Lee Brown came out to be first choice," new Houston Mayor Kathy Whitmire said in an interview. "He is a man who twice before has come in as a chief executive from the outside and made major improvements, once in Atlanta and earlier in Portland, Ore."

Brown, Houston's first black police chief, inherits a force suffering from low morale, a poor public image and reputation for brutality toward minorities. In recent years, several complaints of civil rights violations have been filed against Houston police officers. The 3,000-man force includes about 250 blacks.

The department also is at war with Whitmire, who has been mayor for three months and wants to revamp its system of management and improve performance. Whitmire said of Brown, "He has provided the leadership that will allow us to accomplish the goals I set out during my campaign."

Deputy police chief Fred Bankston said reaction among fellow officers to Brown's hiring was bad. "They say it's a slap in the face," he was quoted as saying. "It causes the men to lose incentive."

The hiring came a day after acting chief John P. Bales asked to be removed from consideration for the job, saying his decision was not related to Whitmire's recent public criticism of the department. Bales had succeeded chief B. K. Johnson, who was under heavy criticism when he resigned late last year.

Brown came to Atlanta in 1978, and the city's crime rate climbed to record levels the next year. By 1980, the overall crime rate had improved, but the missing and slain children of Atlanta became his most troublesome problem.

Brown became a recognized public figure during the investigation, appearing frequently at news conferences. At many of them, he revealed little information about actual developments in the Atlanta murders.