Ultrasonic welding (USW) is one of the methods for producing solid-phase joints of thin metal sheets, which in the future can be used to obtain laminated composite materials, for additive manufacturing and renovation of metallic articles. The quality of joints depends on both the processing conditions and the properties of welded metals and alloys. At present, the USW conditions, the properties, and structure of weld joints of strong metals, in particular, of nickel, are underexplored. In this work, the authors studied the influence of the compressive load magnitude on the lap shear strength and the structure of joints of annealed nickel sheets with a thickness of 0.5 mm produced by spot USW. The authors carried out USW at a vibration frequency of 20 kHz with an amplitude of 15 μm, the time of welding was equal to 2 s. The compressive load magnitude was varied from 3.5 to 7 kN. The study showed that with an increase in the compressive load in the considered range of values, the strength of weld joints increased, reached a maximum, and then decreased. The joints obtained at the compressive load of 6 kN demonstrated the highest lap shear strength of 1950 N. A zone of thermomechanical influence with a gradient microstructure is observed near the contact of the welded surfaces. In a layer with a thickness of 10–20 mm, the initial coarse-grained structure of nickel is transformed into an ultra-fine-grained one with a grain size of less than 1 mm. The ultra-fine-grained layer neighbors on crystallites, the size of which is several micrometers and increases with a distance from the contact surface of welded sheets. The authors compared the results of mechanical lap shear tests and structural studies with the data obtained after ultrasonic welding of nickel, aluminum, and copper alloys.