"There were risks involved in taking funding from sources associated with Libya and they should have been weighed more heavily in the balance," he wrote.
The Gadhafi regime has drawn international condemnation for its violent crackdown on anti-government rebels, who have wrested control of several large cities outside of the capital, Tripoli.
The LSE Council also announced that it has commissioned an outside inquiry into the school's relationship with Libya and with Gadhafi's son, Saif, who received a PhD from the prestigious university in 2008.
The probe will examine, among other things, the "academic authenticity" of Saif Gadhafi's doctoral thesis. Davies said he believes the degree was "correctly awarded," though he said the school is "currently reviewing the evidence."
"And there was no link between the grant and the degrees," he said, according to the letter.
Libya: Spending oil money across the globeIn addition to Saif Gadhafi's academic record, the inquiry will look into the School's decision to accept nearly $2.5 million from the Gadhafi International Charity and Development Foundation in 2009. So far, the LSE has received about $480,000 from the charity.
It will also look into a $3.6 million contract LSE Enterprise, a commercial subsidiary of the university, had with Libya's Economic Development Board to train Libyan civil servants and professionals. That deal included about $32,000 in tuition payments for the head of the Libyan Investment Authority.
The school's acceptance of money from the Gadhafi charity to pay travel expenses for LSE academic speakers is also under investigation.
Peter Sutherland, chairman of the LSE's court of governors, said Davies had been an "outstanding director" during his eight-year tenure at the university.
"His achievements here will endure long after the current controversy has died away," Sutherland said in a statement.
Relax, Libya oil crisis is no big deal - watchdogDr. Charles P. Mouton hopes to build on Meharry Medical College’s legacy