We reconstruct a historical sea level record due to land ice mass changes over the past four decades (1980-2019). Land ice includes polar ice sheets and mountain glaciers and ice caps (GIC). We estimate ice sheet mass changes using a Mass Budget Method, which compares surface mass balance at the interior of Greenland and Antarctica Ice sheets with ice discharge at the peripheral. For glaciers and ice caps, we extend mass changes observations from GRACE (Gravity Recovery and Climate Experiment) and GRACE-Follow On satellites with surface mass balance output products from state-of-art global and regional climate models. In the construction of the forty-year GIC record, we thoroughly account for uncertainties from different sources and correct trend bias in the climate models. We calculate global and regional sea level in response to the land ice mass changes. Land ice mass variations at different locations lead to a non-uniform sea level pattern called sea level fingerprints (SLF). Our record triples the previous observation period of SLF estimates based on GRACE/GRACE-FO alone, improving confidence in the estimates during the common period. Over the past four decades, the GIC contributed a larger mass loss than Greenland and Antarctica, but with minor differences between them. We use the reconstructed land ice sea level record combined with other sea level components to further study the closure of the sea level budget during the recent 15 years (2005-2019). We examine the closure of sea level budget by comparing the total sea level measured by altimetry to the sum of individual sea level components, including steric sea level and SLF induced by mass changes from land water and atmospheric and oceanic non-tidal dynamical processes. We find an excellent agreement between the sum and the total sea level at the global mean scale and in the Pacific Ocean, which suggests closure of sea level at the majority of the global ocean during 2005-2019. The dominant signals are from ice sheets and steric components for the past forty years, but the GIC signal remains significant and cannot be ignored. We expect the 40-year SLF record and the evaluation on the recent 15 years' sea level budget to be of importance to help constrain model physical processes and, in turn, enhance projections of future sea level rise.