The present invention discloses a process for installing a floating platform to the ocean floor using a spoolable (preferably composite) tether, comprising installing the spooled tether onto the floating platform; towing the floating platform to a site for installation; unspooling the tether; connecting a bottom end connector of the tether to a foundation on the ocean floor; and connecting a top end connector of the tether to the floating platform. A preferred floating platform is a tension leg platform, and the invention includes a novel tension leg platform (TLP) comprising a spooled tether installed thereon. In a preferred embodiment the foundation is a suction anchor, and the suction anchor is connected to the bottom end connector prior to unspooling the tether and attached to the ocean floor after unspooling the tether. The floating platform may be uninstalled, moved and re-installed according to the invention.