"I am very delighted to be here in my second home, Juba. We are looking for a very strategic, very distinguished relationship between our two nations, and the sky is the limit for this relationship," said Hamdok, who heads an 18-member transitional government formed after the overthrow of Omar al-Bashir, on Thursday.
He is set to meet South Sudan President Salva Kiir as well as Sudanese opposition leaders during his two-day visit.
"We hope to have a very prosperous relationship that will address issues of trade, border issue, oil, free movement of our people between the two countries and all these agendas."
South Sudan split from the north in 2011 after decades of bloody war with Khartoum, famously becoming the world's youngest nation.
But just two years later, it plunged into its own internal conflict, with catastrophic consequences.
While tensions remain high between south and north over ongoing border disputes and the transfer of oil to the north, the two nations have increasingly moved to normalise ties in recent years.
Analysts say the two have been pushed together by the grinding war in South Sudan, which has defied several peace attempts, and an economic crisis in Sudan, which was hard-hit by the collapse of the south's oil industry.
One of al-Bashir's last moves before he was overthrown was to broker a peace deal between President Kiir and his rival Riek Machar - at a time when much of the world had wearied of trying to solve the crisis.
However, the 2018 peace deal has stalled as Sudan battled its own political crisis in recent months.
According to Al Jazeera's Hiba Morgan, Hamdok said Sudan will be an open space and will build its foreign relations based on common interests.
"Along with trying to make peace with the armed groups, the South Sudanese president and the Sudanese prime minister will be talking about bilateral relations for the interests of the two countries," she said reporting from Juba.
"The economy of these two countries is based on the pumping of the oil and the export of the oil, with South Sudan paying Sudan oil fees which supports the economies of the two countries."
Observers are anxious to see if Khartoum's new government will push Kiir and Machar to advance on the implementation of the deal.
The two men met this week in Juba for the first time in five months, with a power-sharing government meant to be set up by November.
In a further sign of rapprochement between the two countries, Kiir offered in 2018 to mediate peace talks between Khartoum and rebels in the Blue Nile, South Kordofan and Darfur conflict zones.
The Blue Nile and South Kordofan fought alongside the south for independence. However, these areas were left north of the border in 2011 and have since witnessed an armed campaign against Khartoum.
Rebels in Darfur also waged a long war over marginalisation in the western region.
Hamdok has promised to end these conflicts which have left thousands dead and millions displaced.
"When he was appointed, he made a pledge that his transitional government will prioritise peace over anything else, and will try to achieve it within the first six months of the 39-month transitional period," Morgan said.
This week, armed groups from those areas held talks in Juba which ended on Wednesday in the signing of a deal on "pre-negotiation principles" with Khartoum.
"We assure them and the people of Sudan in general that all the suffering and the killing and marginalisation will end," said General Mohamed Hamdan Dagalo, the deputy chairman of Sudan Sovereign Council.