Prime Minister Ehud Barak expressed his gratitude to Clerides.
"The act of the president…was greatly appreciated by the people of Israel and will serve the advancement of good neighborly relations that prevail between Israel and Cyprus," Barak said.
With the pair's release, there is speculation that Israel has promised to help Cyprus in its efforts to join the European Union.
The agents were arrested immediately after Israeli President Ezer Weizman's state visit to Cyprus last November.
Israel has quietly been working for their release ever since they were arrested with sophisticated listening equipment close to a military base.
The Mossad men were captured at a sensitive time when Cyprus was threatening to place Russian S-300 surface-to-air missiles as protection against Turkish jets at a base the Mossad agents were believed to be monitoring. It was coupled with reports that Israel had been training Turkish pilots on how to avoid the SAM missiles.
At a much reported trial, Damary and Hargov were convicted on Feb. 1 of approaching a prohibited military area near Ziyi in southern Cyprus and sentenced to three years.
They were also sentenced to a concurrent term of six months for possessing wireless scanning equipment without a license.
The two pleaded guilty to the lesser charges after the prosecution dropped charges of conspiracy and espionage in an apparent plea bargain deal. The more serious charges carry a sentence of up to 10 years.