A wellhead foundation is for one or more subsea wells. The wellhead foundation has a suction foundation with a housing with an open bottom and a top which is closable with a top cover, and one or more pipes being attached to the housing and extending from the top of the housing and at least over a substantial part of the vertical extent of the housing and away from the housing at least in a vertical direction. A straight upper part of each pipe projects up above the top of the housing and forms an upper conductor-casing portion which is arranged to receive the upper well-pipe portion and forms part of a low-pressure barrier in the well. The straight upper pipe portion of each pipe is arranged parallel to the center axis of the housing. A method of establishing a subsea wellhead foundation is described as well.