Togo withdrew from this year's tournament in Angola after two members of their delegation and the team bus driver died in an ambush in the province of Cabinda.
While the world expressed horror and sympathy, African football's governing body slapped them with a four-year ban, saying they had not properly withdrawn from the tournament and that the players had been forced home because of the pressure of their government.
"This decision is good news for us - it gives us a real bounce," Elitsa Lanou, technical director of the Togo team, said in a statement.
"If the sanction had been upheld, we would have been knocked flat. Now we have to organise and move on."
Blatter was asked to broker a solution after Togo appealed to the Swiss-based Court of Arbitration for Sport against the ruling keeping them out of the 2012 and 2014 events.
"This shows we can solve our internal disputes within the football family for the benefit of all those who are involved in our game and in particular for the players," Blatter said in a FIFA statement.
Although the agreement says CAF's president Issa Hayatou must still ask his executive committee to squash the sanction, that should be a mere formality given his position of authority.
Togo have agreed in return to admit they did not follow proper procedure in withdrawing from the Nations Cup.
Togo's star player Emmanuel Adebayor announced his retirement from international football in the wake of CAF ban but might now be persuaded to return.
CAF left Togo out of February's draw for the 2012 Nations Cup qualifiers but have an open berth in one of the groups that they are expected to place the Togolese in.
CAF's executive committee meets in Cairo next week when the Togo ban should be formally rescinded.
