The ISOLDE RIB-facility at CERN has today been producing a vast range of radioactive beams since more than 30 years. The low-energy beams of ISOLDE will be complemented by a post-accelerator, REX-ISOLDE, currently being assembled. In order to convert the pseudo-DC, singly-charged beam from the ISOLDE mass separators into a cooled and bunched beam at higher charge states a novel scheme of trapping, cooling and charge-state breeding has been devised, using a linear Penning trap and an Electron Beam Ion Source (EBIS). This allows for subsequent acceleration by a short, cost-effective LINAC consisting of an RFQ, an IH-structure and three seven-gap resonators, reaching 0.8 - 2.2 MeV/u. The installation of REX-ISOLDE is well underway and the first post-accelerated radioactive beams are expected to be obtained during late 2000