The Pentagon has reversed field and decided to send one of its officials a letter of reprimand rather than fire him for allegedly mishandling classified information that ended up in a Washington Post article on the projected cost overrun on President Reagan's rearmament program.

The official, John C. F. Tillson, director of manpower management, failed three lie detector tests ordered by Deputy Defense Secretary Frank C. Carlucci in an attempt to find the source of The Post article of Jan. 8.

The article disclosed that an internal Pentagon study estimated that it could cost $750 billion more than the $1.5 trillion projected to buy the forces the Joint Chiefs of Staff said it would need to carry out Reagan's military policies in the five fiscal years 1984 through 1988.

Tillson denied that he was the source for the article, or had discussed classified information with any unauthorized people. However, his boss, Lawrence J. Korb, assistant secretary of defense for manpower, notified him on March 9 that the Defense Department intended to dismiss him for "your disclosure of official information to unauthorized persons and your disregard of Department of Defense regulations and procedures for the protection of classified information."

Since then, the unauthorized persons to whom Tillson was accused of disclosing information have filed sworn statements denying that this was the case; the author of The Post article, staff writer George C. Wilson, wrote Defense Secretary Caspar W. Weinberger that Tillson was not his source; a group of senior Pentagon civilian executives protested in a letter to Weinberger that Tillson was being treated unfairly, and Sen. Sam Nunn (D-Ga.) sent Carlucci an assessment by Senate lawyers of how the Pentagon legal case against Tillson was flawed.

James Heller, Tillson's lawyer, said yesterday that the Pentagon decision to settle for a letter of reprimand and restore Tillson to his job with security clearances intact represented "complete vindication, although I would rather have seen them send him a letter of apology."

The Pentagon had no comment on the case, the administration's first high-profile investigation of a newspaper leak.