You can also install GDAL utilities from:

https://www.gdal.org/gdal_utilities.html

then use from command line:

gdal_translate -of AAIGrid elevation_data.tif elevation_data.asc

M. Wasif Naqvi free 30m global DEM data is available on glovis.usgs.gov. You need to get yourself register with them to use the data. This data is available in Tiff format as you require.

You can get this data for past many years. 2000 and beyond

tiff format can be converted to Ascii format using ArcGIS conversion toolbox or in QGIS (Free software).

With ArcMap that import capability is found within the ASCII to Raster tool. This tool converts an ASCII file representing raster data to a raster dataset.

Read this document for detailed information:

https://library.ryerson.ca/gmdc/files/2014/08/1_AsciiToRaster_ArcMap9.pdf