The finance ministry said 85.8% of its €177 billion in bonds regulated under Greek law had been tendered, adding that the rate would reach 95.7% with the use of collective action clauses to enforce the deal on creditors who refused to take part voluntarily.
The result should clear the way for the European Union and International Monetary Fund to release a €130 billion bailout package agreed with Greece last month.
Government spokesman Pantelis Kapsis said the result was a "vote of confidence" in Greece's ability to carry out deep structural reforms to its stricken economy. "I think it's a historic moment," he told private television station Antenna.
The biggest sovereign debt restructuring in history will see bond holders accept losses of some 74% on the value of their investments in a deal that will cut more than €100 billion from Greece's crippling public debt.
The deadline for acceptance of the offer for bonds governed by international law and for state-guaranteed bonds issued by public companies has been extended to March 23.
Athens confirmed it would enforce the deal on all its bondholders, activating the collective action clauses on the bonds regulated under Greek law.
That may trigger payouts on the credit default swap (CDS) insurance that some investors held on the bonds, an event which would have unknown consequences for the market.
The Institute of International Finance, the bank lobby that negotiated on behalf of Greece's private creditors said: "The debt exchange results, and the associated unprecedented upfront nominal reduction in the privately-held Greek debt, will catalyse the ... official sector support for Greece's new three-year reform programme," it added.
Despite the success, the deal will not solve Greece's deep-seated problems and at best it may buy time for a country facing its biggest economic crisis since the second world war and crushed under debt equal to 160% of its gross domestic product.
Athens must have the funds in place by March 20 when some €14.5 billion of bond repayments are due, which it cannot hope to repay alone.
Greece has staggered from deadline to deadline since its crisis broke two years ago and several of its international partners have expressed open doubts about whether its second major bailout in two years will be the last.
Analysts were cautiously optimistic, but acknowledged the bond swap was unlikely to draw a line under Greece's troubles.
Underlining the severe problems facing Greece after five years of deep recession, data on Thursday showed unemployment running at a record 21% in December, twice the eurozone average, with 51% of young people without a job.