The stringent COVID-19 lockdown measures in 2020 significantly impacted people's mobility and air quality worldwide. This study presents an assessment of the impacts of the lockdown and the subsequent reopening on air quality and people's mobility in the United Arab Emirates (UAE). Google's community mobility reports and UAE's government lockdown measures were used to assess the changes in the mobility patterns. Time-series and statistical analyses of various air pollutants levels (NO2, O3, SO2, PM10, and aerosol optical depth-AOD) obtained from satellite images and ground monitoring stations were used to assess air quality. The levels of pollutants during the initial lockdown (March to June 2020) and the subsequent gradual reopening in 2020 and 2021 were compared with their average levels during 2015-2019. During the lockdown, people's mobility in the workplace, parks, shops and pharmacies, transit stations, and retail and recreation sectors decreased by about 34%-79%. However, the mobility in the residential sector increased by up to 29%. The satellite-based data indicated significant reductions in NO2 (up to 22%), SO2 (up to 17%), and AOD (up to 40%) with small changes in O3 (up to 5%) during the lockdown. Similarly, data from the ground monitoring stations showed significant reductions in NO2 (49% - 57%) and PM10 (19% - 64%); however, the SO2 and O3 levels showed inconsistent trends. The ground and satellite-based air quality levels were positively correlated for NO2, PM10, and AOD. The data also demonstrated significant correlations between the mobility and NO2 and AOD levels during the lockdown and recovery periods. The study documents the impacts of the lockdown on people's mobility and air quality and provides useful data and analyses for researchers, planners, and policymakers relevant to managing risk, mobility, and air quality.