Eyadema died on Saturday after 38 years in power and Togo's army chiefs immediately invested his son Faure Gnassingbe as president.
The military has suspended the constitution, which stipulates the head of the national assembly should assume power on the death of the president with elections held within 60 days.
The influential African Union (AU) condemned the move and its President Alpha Umar Konare called the installing of Gnassingbe's son by the army a military coup.
Sidi Amin, editor-in-chief of Senegal's al-Fajr newspaper, told Aljazeera Gnassingbe was preparing for his son to become his successor and amended the constitution by lowering the age of president from 40 down to 35.
"[The military's action] is a contradiction of our constitution and local laws," Olympio said from Paris, where he has been living since an attempt to assassinate him in Togo in 1992.
"We need to have these free and fair elections as soon as possible," he said, adding he would consider running.
Olympio's father, Sylvanus, was Togo's first post-independence president but he was killed in a 1963 coup led by Eyadema, who was then a 27-year-old army sergeant.
Sylvanus said it was encouraging that world leaders also condemned the military government, and called for greater
"France has to put pressure on the junta to open up the political process and we need to work hand in hand with the European Union to have these elections," Olympio said.
France's Chirac maintained close
ties with Togo's autocratic ruler
He cautioned that a poll would not be easy to organise. "It is a one-party parliament and that in these circumstances, even with the best will in the world, you can't organise free and fair elections within 60 days," he said.
Olympio added that he planned to return to Togo after consulting his party, the Union of Forces for Change, and other opposition parties on a plan to confront the new regime.
When asked whether there would be any foreign interference Amin said it was difficult to say.
He said: "There might be foreign pressure but the army and the son's influence are great."
The Togolese dissident described French President Jacques Chirac's praise for Eyadema, Africa's longest-serving leader, as "unfortunate".
France had maintained good military ties with Gnassingbe's government but has now spoken out against the succession.
In the last several years Togo's government has been slapped with sanctions from Europe, the US, the World Bank and the International Monetary Fund.
The European Union froze aid in 1993 because of what it called "democratic deficiencies".