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Morsi will meet with President President Asif Ali Zardari during the one-day visit, the first to Pakistan by an Egyptian leader since Gamal Abdel Nasser in the 1960s, Pakistan's foreign ministry said.
The ministry said the visit is a "watershed and a landmark" in relations between the two Muslim nations which would "give a new impetus to economic, trade and cultural relations".
"President Morsi's decision to choose Pakistan as the first South Asian country for a bilateral visit manifests Egypt's desire to add a new chapter to its bilateral ties with Pakistan," it added.
Officials from the two countries signed agreements to promote cooperation in shipping, investment, information technology and science and technology.
Pakistani state television showed live footage of the ceremony at the presidential palace where Morsi was greeted and presented with a military honour guard.
Late Monday he is due to travel to India, where he will meet with Prime Minister Manmohan Singh and business groups to bolster a blossoming trade relationship worth $4.5 billion in 2012/11 compared to $3.2 billion the previous financial year.
"Our trade with Egypt has increased so rapidly in the last three years that India is now Egypt's seventh-largest trading partner," India's ambassador to Egypt Navdeep Suri told reporters ahead of the visit.
"We talk often in general terms about space, technology and cooperation but during this visit we are talking in specific terms about launching an Egyptian satellite," he added.
Egypt is struggling to restore investor and foreign lenders' confidence in the nation, which has suffered a sharp economic decline since the uprising that overthrew president Hosni Mubarak in February 2011.
Morsi's administration has been plagued by unrest and deadly clashes between protesters and police, blocking efforts to build broad-based support for a needed program of economic reform.