Virginia Gov. Charles S. Robb announced today that Public Safety and Transportation Secretary Franklin White will resign next month to become New York state commissioner of transportation.

For two years White has been embroiled in prison problems that have plagued Robb's administration, including last year's brief escape of six death-row inmates from the prison at Mecklenburg, several disturbances by inmates and the resignation of two corrections department chiefs.

White joined the administration as secretary of public safety and assumed the duties of the transportation secretary under a cabinet reorganization last year.

White, 44, the only black in Robb's cabinet, will be replaced by Secretary of Administration Andrew Fogarty, 39. Fogarty's current duties will be assumed by Robb's chief of staff, David A. McCloud, for the rest of Robb's term which ends in January.

White, the first cabinet member and fourth high-ranking Robb official to leave the administration this year, will resign effective July 15, according to the governor's office.

The appointment of McCloud, who is paid $68,496 a year, is an example of his influence over the state's bureaucracy.

Former administrative secretary Wayne Anderson left that post last year during a cabinet shakeup in which he complained privately that McCloud had usurped his authority.

Fogarty, who is paid $67,496, had joined the staff of Gov. John N. Dalton, a Republican, after working with the state legislature.

Robb subsequently asked Fogarty to remain as transportation secretary.

In a joint announcement today, Robb and New York Gov. Mario Cuomo said that White, a former New York state deputy budget director, would oversee New York's 12,000-employe transportation department at a salary of $81,200, or about $14,000 more than his current salary.

"Frank White has been a distinguished cabinet member and has served Virginia with uncommon ability," said Robb. "I am pleased that he now has a challenging opportunity to continue his public service in New York."

The New York agency maintains 15,000 miles of road, a 160-year-old canal system and two airports, as well as regulating intrastate bus systems and running intercity rail services.

White was sharply criticized last August by Alvin J. Bronstein, director of the American Civil Liberities Union's National Prison Project, after state officials threatened to use force to quell an inmate riot in which hostages were taken.

The prison uprising later ended peaceably.

Earlier, White had clashed with Corrections Director Ray Procunier over a budget issue that led to Procunier being disharged by Robb.

Following the escape of prisoners on death row and other disturbances at Virginia prisons, Robert Landon quit as corrections chief.

Landon was succeeded by Allyn Sielaff, White's deputy.

Before joining Robb at the start of his term in 1982, White lived in Silver Spring and served as a White House liaison official under President Carter.

White previously worked for the New York city government and the NAACP Legal Defense Fund. He is a graduate of Columbia Law School and the City College of New York.