An offshore oil well riser system comprises one or more tubular conduits suspended from a floating platform and having bottom ends extending downward substantially vertically toward the sea floor. A bottom end connection and tensioning assembly is disposed at the bottom ends of the conduits and comprises a jumper for connecting the bottom end of each conduit to an associated sub-sea oil well, a weight for applying a vertical tension in the conduits, and an apparatus for constraining the bottom end of the conduits against horizontal movement, while enabling them to move freely in a vertical direction and to pivot freely at their bottom ends in response to motions of the platform on the water surface. The riser system is useful with a wide variety of floating platforms, and can be employed in either dry tree or wet tree completion systems.