Kuznetsov, 50, who worked for the United Nations Advisory Committee on Administrative and Budgetary Questions, was arrested in September 2005 after borrowing $300,000 from a Russian colleague, allegedly aware that the funds had been acquired by criminal means.
"We are satisfied with this decision," a spokesman for the Russian Foreign Ministry said, without specifying the date of Kuznetsov's return to Russia.
Kuznetsov held diplomatic immunity as a UN employee, but the status was revoked by Kofi Annan, the secretary general at the time, paving the way for the FBI to arrest him.
The ex-diplomat was sentenced in October of 2007 by a U.S. district court, and was ordered to pay a total of $73,000 in fines.
A district court in New York confirmed that on October 31 a payment of $73,000 was received, a requirement for the court to begin considering his return to Russia.
Kuznetsov, who has always denied the charges, is currently serving his term at Allenwood Federal Correctional Institution in Pennsylvania.
