A passive MRI-compatible guidewire includes an elongate, flexible tubular shaft, an elongate core wire of non-ferromagnetic material, and an elongate spring coil of non-ferromagnetic material axially surrounding the elongate core wire to form a distal end portion. The core wire includes opposite first and second end portions separated by an intermediate portion. The intermediate portion has a round cross-section, and the first and second end portions each have a non-round cross-section. The first end portion of the core wire resides within an inner lumen of the tubular shaft and is secured therewithin. The spring coil includes opposite first and second ends, and the spring coil second end is secured to the core wire second end portion via polymeric material that forms a rounded distal tip of the guidewire. The guidewire includes a plurality of spaced-apart, passive MRI-visible markers.