The visit was Bashir's first to his southern neighbor since South Sudan became independent in 2011, the BBC reported.
South Sudan gained about 75 percent of Sudan's oil production upon becoming a state, and the countries have disagreed over how much Juba, the South Sudanese capital, should pay to move the oil through pipelines in Sudan. South Sudan shut down production last year, causing stress to the economies of both countries.
Juba relies on oil exports for 98 percent of its budget, while Khartoum, the capital of Sudan, needs the revenue for foreign currency and to make up for a budget deficit, the Financial Times reported.
Both sides struck a deal this month, and oil is expected to begin flowing again at the end of May.
During the meeting in Juba, both leaders are expected to meet with technical experts from oil companies and reopen an oilfield to production, the Times said.
Bashir and Kiir still have not reached agreement on who owns Abyei province and other regions along their 1,200-mile border.
Notable deaths of 2014 [PHOTOS]
Mexico mayor, wife blamed for missing students