In 1987 Wemba signed a solo worldwide management deal with Japanese promoters. Consequently it was necessary that both he and Viva La Musica relocate from Zaire to Paris, where Wemba could better promote fully his dream of becoming an internationally known singer. Much speculation on the future of Viva La Musica followed, with many wondering if Papa had finally abandoned his African fans in search of a wider audience. Upon leaving Kinshasa, Wemba was accompanied by an inner core of Viva musicians. He then began recording with French producer, Martin Messonier. The Viva musicians remaining in Kinshasa were sent airline tickets and asked to join Wemba. Slowly, as Wemba relocated himself to a new permanent European base, the rest of the band began to follow. The fruits of Papa's labours with Messonier appeared in 1988 on his first world music LP, titled Papa Wemba (Sterns). The disc is essentially a 'best of' LP featuring newly recorded versions of some of his biggest hits with Viva La Musica since 1977. To promote his new international music live Wemba started a new, non-Zairian band called first Viva, and later, Molokai International. In late 1988, he returned to Japan to fulfil the cancelled 1986 second tour dates. In 1989 Wemba also gave his debut performances in London and New York, backed by his new band. With Molokai International, Wemba then went on to undertake world-wide tours as an integral part of the successful WOMAD (World Of Music And Dance) international music and performance packages. One reason Wemba gave for the formation of Molokai International was that he found many Zairian musicians, in his own words, "limited in their abilities to work with other, non-African, musics," adding that he wanted to take his music beyond Africa. "The only handicap of Zairian musicians is that they don't listen to music from outside of Zaire, like music that is done in Europe, the United States or other African countries," Wemba explained in a 1990 interview. "Zairian musicians tend to play only Zairian music. First of all it's because of a lack of promotion of outside musics since Zairian radio, from morning until night, broadcasts only Zairian music. This makes Zairian musicians very limited. It is necessary to be open minded and there are very few who have that spirit." In 1991 Wemba signed a solo deal with Peter Gabriel's Real World Records. Since then he has made three Real World LPs, 1992's Le Voyager, 1995's Emotion and the 1998 live LP, Molokai. Other collaborative world music projects include the 1997 single "So Why" made for the International Red Cross. Wemba and Molokai International continue to undertake benefit concerts for organisations such as Médecins Sans Frontières, Rock Against Racism, and a host of other campaigns involved with fighting Third World debt, famine and other core problems such as HIV-related illnesses in Africa.

He has also continued touring the world with Molokai International, having played extensively across Europe, North and South America, Asia, and headlining at WOMAD shows in Sidney, Okinawa, and New York's Madison Square Garden. International collaborations with other musicians have included Peter Gabriel, Stevie Wonder, Youssou N'dour, Lucky Dube and South African vocalist Brenda Fasi, among a host of others.