We present a lambda-870-mu-m map and ON-OFF measurements of Sgr A* and determine its flux density to be S870-mu-m = 4.8 +/- 1.2 Jy. We confirm flux densities of S1300-mu-m = 2.6 +/- 0.6 Jy and S350-mu-m = 18.5 +/- 9 Jy derived earlier (Zylka & Mezger 1988; Mezger et al. 1989). We reanalyse previously published and unpublished high-resolution flux density measurements to determine its spectrum from radio wavelengths to the Near Infrared (NIR). The radio spectrum for nu less-than-or-equal-to 10 GHz increases slowly with frequency to approximately 1 Jy, then levels off and must turn over in the frequency range 2 10(2) GHz < nu < 1.5 10(4) GHz. The submm/FIR/MIR spectrum increases steeply with frequency, attains a maximum of greater-than-or-equal-to 20 Jy in the range 7 10(2) less-than-or-equal-to nu less-than-or-equal-to 1 10(4) GHz, and drops below 0.1 Jy at lambda less-than-or-equal-to 20-mu-m. The NIR spectrum appears to rise from S2.2-mu-m approximately 0.06 Jy is-proportional-to nu(2) (Eckart et al. 1991). This spectrum is modelled by three components: 1) an optically thin synchrotron source of size approximately 10(14) cm for the radio spectrum (Lesch et al. 1988: Melia 1991), 2) an optically thick dust disk of outer radius R approximately 10(17) cm or a self-absorbed synchrotron source of size approximately 6 10(12) cm for the FIR/submm spectrum, 3) an opaque thermal plasma of T(e) approximately 37000 K and size approximately 1.5 10(12) cm for the NIR spectrum. A black hole of approximately 1 - 2 10(6) M. surrounded by a thin (H/R approximately 10(-3)) disk accreting M approximately 10(-6) M. yr-1, would explain the presence of these three components within the inner arcseconds of the Galactic Center.