The U-turn came after the North East Fife MP Stephen Gethins urged the Home Office to reconsider its decision which stopped the men from taking part in a Church of Scotland training programme.
He said the government must take a good look at how it deals with these kinds of applications in future.
He said: "Time after time visas are being denied to people with genuine reasons for entering this country. This costs them time, money and energy and while I welcome the fact that the Home Office has now granted access, it is simply not good enough that people have to jump through so many hoops to get here.
"I wish all those involved in the peace mediation programme well. This is a great initiative by the Church of Scotland on an area that has been so badly affected by conflict. The Government should be getting behind this work rather than adding more obstacles. "
Mr Gethins had urged the Home Secretary on Wednesday to personally intervene to ensure they could attend the "vitally important" mediation and conflict resolution workshops with nine other members of the Presbyterian Church of South Sudan.
The programme is aimed at empowering faith leaders to help bring peace to the war torn African country, which became the newest nation in the world in 2011.
One of the pastors, Rev Orozu Daky, said he was "deeply disappointed" because it is was the first time he had ever been denied a visa, despite visiting Germany and Switzerland more than six times, the USA twice and Scotland once.
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