Twelve accords were signed at the outset of his two-day visit to Khartoum, including economic and military deals as well as on the creation of a strategic cooperation council, Erdogan told a news conference.
He said the two Muslim countries aimed at boost two-way trade from the current level of $500 million a year to $1 billion in an initial stage and then $10 billion.
Bashir hailed the trip by Erdogan, who is to travel on to Chad and Tunisia, as an "historic" first visit to Sudan by a Turkish president.
Sudan's leader, who is wanted by the International Criminal Court on charges of genocide and war crimes in the strife-torn Darfur region, earlier this month attended a summit in Istanbul of the Organisation of Islamic Cooperation.
Erdogan called on those at the summit to condemn US President Donald Trump's recognition on December 6 of the disputed city of Jerusalem as Israel's capital.