A bottom-to-surface connection installation for an undersea pipe. The installation comprises a vertical riser having its bottom end connected to an undersea pipe on the sea bed, and having a float at its top end, and a pipe connecting a floating support at the top end of the vertical riser. The connection between the riser bottom end and the undersea pipe is via an anchor system having a base on the sea bed. The base holds and guides junction elements between the bottom end of the riser and the end of the lower end of the undersea pipe. The junction elements comprise a rigid pipe element presenting an angled bend and a pipe coupling element which are fixed to a moving support of the base. The junction elements are fixed to the moving support and are free to move only in translation in a single longitudinal direction.