One of the four condemned men is the son of a leader of Ansar al-Sunna, an Islamist group, which is linked to Wahhabism - a form of Sunni Islam practised mainly in Saudi Arabia.
A group calling itself Ansar al-Tawhid had claimed responsibility for the murders, SITE, an organisation which monitors Islamist websites, said.
It said the murder was in response to attempts to raise the banner of Christianity over Sudan, the largest country in Africa.
Ahead of the verdict, the US embassy in Khartoum had urged personnel and citizens to keep a low profile if the court found the defendants guilty.
"Should the court announce guilty verdicts in this case on June 24, the reaction among the men's supporters could include demonstrations at Embassy Khartoum facilities and/or other anti-American, anti-Western actions," the embassy said in a statement.
"US citizens are advised to avoid the Khartoum North courthouse, located in downtown Khartoum, maintain a low profile, and increase vigilance," it said.