This is how I ended up solving it:
cols = array.shape[1]
rows = array.shape[0]
originX = 85 # starting longitude, top left
originY = -60 # starting latitude, top left
driver = gdal.GetDriverByName('GTiff') # load the GTiff driver
outRaster = driver.Create(fileName, cols, rows, 1, gdal.GDT_Int16) # create the raster layer
outRaster.SetGeoTransform((originX, pixelWidth, 0, originY, 0, pixelHeight))
outband = outRaster.GetRasterBand(1)
outband.SetNoDataValue(-1)
outband.WriteArray(array) # write the binary file to the TIFF
outRasterSRS = osr.SpatialReference()
outRasterSRS.ImportFromEPSG(4326) # import the EPSG projection
outRaster.SetProjection(outRasterSRS.ExportToWkt()) # sets the projection for the tiff
outband.FlushCache() # flush the cache
.bin
. The span is given as outside information.