The ceasefire agreement says all forces should "immediately freeze in their locations", halt actions that could lead to confrontation and release political detainees as well as abducted women and children.
South Sudan's leaders fought for decades for independence, but once they achieved it in 2011, a power struggle between Kiir and Machar led to all out civil war.
A ceasefire between South Sudan's warring parties went into effect just after midnight on Sunday, in what is the latest bid to end a devastating four-year war.
Government and several armed groups signed a ceasefire deal on Thursday during peace negotiations in Addis Ababa, to begin from 00:01 hours (South Sudan local time) on December 24.
The agreement says all forces should "immediately freeze in their locations", halt actions that could lead to confrontation and release political detainees as well as abducted women and children.
Riek Machar, the former vice president whose falling out with President Salva Kiir kick-started the conflict in December 2013, has ordered his rebel forces to "cease all hostilities".
In a statement released on Friday he said all forces should "remain in their bases and to act only in self-defence or against any aggression".
The war
South Sudan's leaders fought for decades for independence, but once they achieved it in 2011, a power struggle between Kiir and Machar led to all out civil war.
A peace deal was signed two years later but it collapsed in July 2016 when fresh fighting in the capital Juba forced then first vice president Machar into exile.
The opposition split, with Taban Deng taking over as first-vice president, while Machar's faction returned to battling the government in the bush.
While the initial fighting pitted Kiir's ethnic Dinka against Machar's Nuer, the renewed violence has metastasised with new opposition armed groups forming.
Peace talks
Violence spread to the southern region of Equatoria, forcing over a million South Sudanese to flock to neighbouring Uganda and the Democratic Republic of Congo in what has become the biggest refugee crisis on the continent.
The latest round of peace talks, which the United Nations described as a "last chance" for peace in the country was pushed by the regional IGAD group as a revitalisation of the 2015 deal.
In addition to Kiir's government and Machar's SPLA-IO, this round of peace talks also includes half a dozen armed opposition groups that have sprung up since July 2016.
A permanent ceasefire is the first step in negotiations to include a "revised and realistic" timeline to holding elections.
The initial peace deal planned for elections in August 2018 — a date seen as unfeasible by many observers.