A knotless anchor for attachment of tissue to bone includes a rigid anchor body and a suture extending there from. The suture is hollow and includes a fixed limb portion secured to the rigid anchor body. A soft suture tunnel extends in a longitudinal direction through the fixed limb portion of the suture. A free suture limb is passed through the tissue, back to the anchor, and through the soft suture tunnel, thereby creating a closable suture loop around the tissue. Tension applied to the free suture limb closes the suture loop, and approximates the tissue to the anchor body. When the anchor is deployed in a bone hole, external features of the anchor body grip the walls of the bone hole and simultaneously compress the suture, thereby preventing tissue pull-out. Anchor assemblies and methods of tissue fixation are also disclosed.