Using a shawl stained with the blood of one the Ripper's victims scientists were able to extract not only the DNA of of Catherine Eddowes (the victim) but a second DNA sample as well. That sample was analyzed against DNA samples of decedents of the known suspects from the Ripper killings and a positive match was found... that of Aaron Kosminski. Kosminski was a polish immigrant fleeing Russian persecution with his family when they arrived in the White Chapel sections of London in 1881. While he was never arrested due to a lack of physical evidence, he was a prime suspect in the murders. Later in life he was committed to an asylum where he died in 1919.
The results of DNA testing have not yet been researched and checked by the academic community resulting in many people not yet comfortable with claiming that this is conclusively the Ripper. However once these results are placed under the scrutiny of the experts we may finally be able to put to rest one of the greatest mysteries of the modern age.