Akayev, 60, formally stepped down in a subdued ceremony at the Kyrgyz embassy in Moscow Monday, where he fled the Central Asian country after the coup on March 24.
The resignation agreement guaranteed Akayev that he would not face prosecution for any wrongdoing committed during his 14-year tenure as the country's first post-Soviet leader, The New York Times reported Monday.
"Askar Akayev has already signed the (resignation) statement," Bermet Bukasheva, a member of a Kyrgyz delegation dispatched to Moscow to negotiate with the ousted leader, told reporters in Moscow.
"Before resigning, he made his final address to the Kyrgyz people asking them to pardon him if he did anything wrong to the nation or individuals and expressed his wish that Kyrgyzstan's future course be as democratic as possible," she added, according to a Reuters report.
Akayev's 18-minute videotaped resignation speech will be broadcast on television and played before the Kyrgyz parliament on Tuesday, when his resignation goes into effect.
By stepping down, Akayev removes the last major obstacle to holding new presidential elections, tentatively scheduled for June 26. If he had not agreed to formally resign, the legitimacy of such elections would be open to question, the Associated Press reported.
"The revolution has taken place, the new government is working, but this document is necessary" to make it legal, Kyrgyz lawmaker Tashkul Kereksizov, who helped arrange the resignation deal, told the AP.
Kereksizov also said Akayev recognized the new authorities. "He said he will not confront the new government in either words or deeds and wished it success," the lawmaker added.
The coup capped weeks of opposition protests fueled by allegations that Akayev manipulated the results of last month's parliamentary elections to ensure a compliant legislature, the AP reported.
Protesters led by Kurmanbek Bakiyev, currently the acting president, also accused Akayev of increasing authoritarianism and running a corrupt regime while people sank into poverty.
Bakiyev welcomed the resignation and said new elections could be held without any fear of violating the constitution.
"This is good. It should have been done before, but obviously he had to think and analyze the situation for a long time," Bakiyev told Reuters in an interview.
Bakiyev and Felix Kulov, a key opposition leader, are expected to run in the upcoming presidential election, Reuters reported. Under the constitution, new polls must be held within three months of the resignation of the previous leader.
Following the coup, Kyrgyzstan's political crisis deepened as the previous and newly elected legislatures vied for legitimacy. Akayev's overthrow also sparked social turmoil, marked by two nights of gunfire and looting in which at least three people were killed.
The tensions began to subside last week when the old parliament eventually ceded authority.
Akayev's plans, including whether he will return to his home country, remain unclear.