A mooring system for securing a floating vessel to the sea floor comprises a plurality of mooring legs, at least one of which includes separate first and second mooring lines. The first mooring line comprises a first end which is connected to the vessel and the second mooring line comprises a first end which is secured to the sea floor. The mooring system also comprises a connection and tensioning device which includes a body, a bore which extends through the body, a chain stopper for adjustably securing the first mooring line to the body, and a connector for connecting a second end of the second mooring line to the body. In use, a second end of the first mooring line is inserted into the bore and the first mooring line is pulled through the bore while the body is subject to an opposing pulling force. Once the first mooring line is pulled through the bore a desired distance, the chain stopper maintains the first mooring line in position relative to the body to thereby secure the vessel to the sea floor.