In the largest reported decrease in 23 years, the number of serious crimes in the United States last year fell 7 percent, according to a report released yesterday by FBI Director William H. Webster.

The decrease is the largest since the FBI began compiling annual crime statistics in 1960, and it follows a 3 percent decline in 1982, the first time crime has decreased for two consecutive years.

The figures released yesterday by the FBI were virtually identical to statistics released last April on a preliminary basis.

Experts have attributed the decrease largely to the aging of the "baby boom" population, which has outgrown the crime-prone teen-age years, and to the large number of criminals behind bars.

According to the FBI survey, 12,070,200 offenses were reported to the police in 1983, with declines in nearly all categories, in every part of the country and in every size community.

Attorney General William French Smith said, "This is a double victory -- the largest one-year decline in the history of the crime index and the first time the index has dropped two years in a row. The numbers tell us we are turning back crime, not just holding our own against it."

The Reagan administration has made fighting crime its priority and an issue in the presidential campaign. President Reagan recently charged that House Democrats had failed to act on his anti-crime initiatives.

The FBI's crime survey has been criticized because it counts only crimes reported to the police. A recent study by the Police Foundation, a research group, found that local arrest statistics often were inaccurate because the police failed to follow the bureau's complex instructions.

In violent crime last year, the FBI found, murder and robbery totals each fell 8 percent; aggravated assaults were down 2 percent. There was virtually no change in the number of forcible rapes.

Among property crimes, burglaries fell 9 percent, larceny and theft 6 percent and motor vehicle theft 5 percent. Arson decreased by 11 percent.

The FBI found that the greatest decline in the crime rate -- 8 percent -- occurred in the Northeast. Other decreases were 7 percent in the South and 6 percent in the North Central and Western regions.

Last year 11.7 million persons were arrested in the United States for offenses other than traffic violations. Among the high-volume offenses were 1.9 million arrests for driving under the influence of alcohol or narcotics, 1.3 million for larceny and theft-related crimes, and 1.1 million for public drunkenness.

Among those arrested, 51 percent were under age 25, and 83 percent were male. Larceny and theft were the offenses for which women were were most often arrested, accounting for 20 percent of all female arrests.

The FBI report includes details on a number of other types of crime:

*Murder. More than 19,000 people were murdered last year. Of every 100 murder victims, 76 were male, 55 were white, 20 were Hispanic and 33 were between the ages of 20 and 29.

Less than half of the murders were committed by strangers. Relatives and acquaintances were responsible for 57 percent of the murders, and 9 percent were committed by spouses of the victims. The most common murder weapons were firearms, with handguns used in 44 percent of the murders. Among the persons arrested in murder cases, 41 percent were less than 25 years old. Half of those arrested were black and 16 percent were Hispanic.

*Robbery. There were 500,221 in 1983. January is the peak month, and robberies ebb in May and June. An estimated $323 million was stolen with an average loss of $645. Of those arrested in robbery cases, 68 percent were under 25 years old, 93 percent were male, 63 percent were black and 36 percent white. Hispanics, part of the white category, accounted for 12 percent.

*Forcible rape. Of the estimated 78,918 cases last year, the highest rate of occurrence was in the summer. About half of those arrested were persons younger than 25, 50 percent were white, 49 percent black and 10 percent Hispanic.

*Burglary. There were an estimated 3,120,842 cases last year, with more in January than any other month. Two-thirds were in residential buildings. Property losses totaled $2.7 billion; the average dollar loss was $860.

Three-fourths of the offenders arrested in burglary cases were younger than 25, and 38 percent were younger than 18. Of all those arrested, 93 percent were male, 67 percent were white, 13 percent were Hispanic and 33 percent black.

The report was based on the reports of 16,000 law enforcement agencies covering 97 percent of the U.S. population.