Being seen as the largest such debt swap in history, the offer calls for investors to be repaid only about a third of their original investments.
Argentina stopped payment on the debt in December 2001 after the country plunge into financial crisis.
Economy Minister Roberto Lavagna announced that 76% of all bondholders had agreed to a six-week-old restructuring offer launched three years after the Latin American country's record default - the largest by any sovereign nation.
The economy began growing again in 2003 and a successful debt swap was seen by markets as key to a sustained recovery.
The move could also potentially reopen credit lines for a country seen as an international financial pariah.