Yale has agreed to pay $7.6 million for allegedly making false claims on federal research grants, the U.S. Attorney’s Office in New Haven said Tuesday, concluding a two-year investigation of Yale’s grant administration.

The investigation, which began in 2006, covered $3 billion in 6,000 grants from 30 federal agencies — including the Department of Health and Human Services, the Department of Defense and the National Aeronautics and Space Administration — between January 2000 and December 2006.

Prosecutors accused Yale of breaking the law by mischarging federal grants in two ways. First, some Yale researchers are said to have improperly transferred grant funds to accounts that were not specifically related to the purpose of the grant. Second, the government alleged some researchers paid themselves for all their summer work, even time and effort unrelated to the grant.

The $7.6 million settlement is half actual damages and half penalties for the false claims, the U.S. Attorney’s Office said.

“This settlement sends a clear message that the regulations applicable to federally-funded research grants must be strictly adhered to,” Acting U.S. Attorney Nora Dannehy said in a statement.

A spokesman for the U.S. Attorney’s Office, Tom Carson, declined to comment on the origin of the investigation.

In a statement Tuesday, the University acknowledged that some errors did occur, particularly with transfers between accounts. As part of the settlement, Yale denied liability for the false claims and was released from it. The government will not sue the University, the U.S. Attorney’s Office said.

The University said in the statement that it cooperated fully with the investigation, producing over a million pages of documents. The Yale Corporation, the University’s highest governing body, bolstered the Audit Committee and required regular reports on research compliance. The University established a committee to oversee audit, internal control and compliance issues.

And in 2006, the University chartered the Office of Research Administration, which developed mandatory training courses for faculty and staff, reviewed policies, introduced a Web-based reporting system, and stiffened oversight of cost transfers.

Andrew Rudczynski, who oversees grants and contracts as Yale’s associate vice president for research administration, did not return a telephone message seeking comment Tuesday.

The thicket of subpoenas, audits and new compliance policies was a source of strain and sometimes a point of contention between faculty members and administrators, who sometimes tended to see the burden of improving grant accounting as resting on each other.

“I recognize that this investigation has been stressful for many members of our faculty and staff, and I also recognize that federal regulations are sometimes burdensome,” University President Richard Levin said in a letter to faculty and staff Tuesday. “We are doing our part to make the regulations more clear and compliance less burdensome.”

Robert Kenney, an attorney at Hogan & Hartson, the Washington law firm that represented Yale, referred questions to Yale’s Office of the General Counsel, which did not immediately respond to a request for comment Tuesday. Shauna King, the vice president for finance, did not return a telephone message seeking comment.

Income from grants and contracts, about $400 million annually, accounts for about a quarter of Yale’s operating budget.