Mali, Mauretania, Burkina Faso, Niger, and Nigeria (N.) are quite easy to explain: trade. If you were an observant, or conversant, Muslim you had access to the massive trade networks of the Islamic world. It followed Berbers to Kanem (near Lake Chad) and across the Sahara with the Sanhaja Berbers if not the Garamites; by the 10th century, there were Islamic communities and even the Ghanas of Wagadu may have been Muslim. This Sudanic Islam was eclectic, and syncretic, focused on the cities; most of the people living in rural areas were not Muslim. So it was an urban, mercantile, wealthy creed. (I assume you don't actually mean "Sierra Leone" as Muslim, because it's really not what with Freetown being a major 1800s Christian center; do you mean Senegal? Same deal there--Takrur and Grand Jolof were powerful Islamic states that adopted the religion via communication and trade.) As people gained more connections on both sides of the desert, they made more; scholars and merchants alike moved across the Sahara, in ever increasing numbers.

Not until the Almoravids tried to take control of the gold from the Bambuk fields that went through Wagadu were there real Islamic invasions across the Sahara. The rise of populist Islam as a true majority creed throughout the region had to wait for the emergence of Sufi orders and the spread of Fulani pastoralists, who embraced the religion's more insular and pastoral, ascetic qualities--so 16th-17th century, really. Those Islamic movements came into conflict with the old urban elites, resulting in a variety of jihads (some militant, some not) aimed at generating a broader shared orthodoxy.

There are a variety of works, but the quick go-to is Nehemiah Levtzion and Randall Pouwels, eds., The History of Islam in Africa (2000). It's big, it's scholarly, it's widely available, and it's cheap.