Saudi Arabia Laser Ranging Observatory (SALRO-7832) has been established in 1995 and is situated in the Arabian tectonic plate which is countering a north east motion. Laser ranging observations of about 20 global SLR stations to LAGEOS-1 and LAGEOS-2 satellites collected for 14 years (1996-2009) have been used to determine Riyadh SLR station positions and velocity. The NASA Goddard's GEODYN-II orbital software has been used to perform orbit determination of these two satellites. The computations were performed on the basis of 114 monthly arcs of observations with the total number of normal points of 33,708 and 40,168 for LAGEOS-1 and LAGEOS-2, respectively. The geocentric coordinates were computed and then transformed to the topocentric North, East and vertical components in reference to the ITRF2008 terrestrial reference frame. The range biases of the Riyadh SLR station in the whole period of study were 2.5 and 2.0 mm with long-term bias stability 7.5 and 7.2 mm for LAGEOS-1 and LAGEOS-2 satellites, respectively. The orbital RMS of fit for all stations was equal to 16.4 mm for the whole period. The stability of the time series positions in form of RMS of the X, Y, Z component residuals w.r.t. a linear trend for Riyadh SLR station were 10.1, 9.3, and 9.0 mm, respectively. 3D deviation from ITRF2008 position was equal to 4.5 mm. The velocities were 29.1 +/- 0.2, 31.6 +/- 0.2, and 1.9 +/- 0.3 mm/year in the North, East and vertical directions, respectively, with a horizontal and 3D velocity 42.9 +/- 0.2 mm/year and azimuth 47.4 +/- 0.8 arc degrees. The central part of the Arabian tectonic plate motion was precisely determined from the Riyadh SLR data and the results showed a good agreement with ITRF2008 velocity, geological model NNR NUVEL1A and with recent GPS estimates. This paper includes a full discussion of the results of Riyadh SLR station collected over 14 years of activity and gives the absolute movement of the central part of the Arabian tectonic plate (velocity and azimuth).