It is possible but would take many years. Luckily it has been done. The link to the regions is below. As is the citation.

Terrestrial Ecoregions of the World (TEOW) is a biogeographic regionalization of the Earth's terrestrial biodiversity. Our biogeographic units are ecoregions, which are defined as relatively large units of land or water containing a distinct assemblage of natural communities sharing a large majority of species, dynamics, and environmental conditions. There are 867 terrestrial ecoregions, classified into 14 different biomes such as forests, grasslands, or deserts. Ecoregions represent the original distribution of distinct assemblages of species and communities.

There are multiple uses for TEOW in our efforts to conserve biodiversity around the world. It provides:

• a map of terrestrial biodiversity that gives enough detail to be useful in global and regional conservation priority-setting and planning efforts.

• a logical biogeographic framework for the development of large-scale conservation strategies.

• a map and descriptions for those working to increase biogeographic literacy and to illustrate conservation issues around the world; including a general description of each ecoregion, outstanding and distinctive biodiversity features, current status and types and severity of threats to the natural habitats.

• a framework for a global species database useful in priority setting and ecological analyses.

• a foundation for the Global 200--a representative prioritization of the world’s most distinctive biodiversity regions

Citation: Olson, D. M., Dinerstein, E., Wikramanayake, E. D., Burgess, N. D., Powell, G. V. N., Underwood, E. C., D'Amico, J. A., Itoua, I., Strand, H. E., Morrison, J. C., Loucks, C. J., Allnutt, T. F., Ricketts, T. H., Kura, Y., Lamoreux, J. F., Wettengel, W. W., Hedao, P., Kassem, K. R. 2001. Terrestrial ecoregions of the world: a new map of life on Earth. Bioscience 51(11):933-938.

http://www.worldwildlife.org/publications/terrestrial-ecoregions-of-the-world

Thank you very much Stuart.

This answer is very comprehensive and precisely helpful. I will go through the document you have attached. I also presumed so, that modelling biomes using remote sensing indeed might be time consuming. At least having that in mind, if I decide to use it then I will have a better planning.

Mapping biomes has been one of the most important cartographic aims for phytogeographers (and geographers) for centuries. It has an old tradition based on field observations (since the XIX century geographers have made biome maps without, of course, satellite images). Now you can use aerial photography, satellites and other resources, but you have to bear in mind that biome maps are an old tradition. And the problem of where to put the boundaries is also an old problem to geographers.

Using GIS some quite different approaches are being developed now. Sarkinen, for example, used "diagnostic" species and species distribution models to map the distribution of Dry Forests in South America (http://www.biomedcentral.com/1472-6785/11/27/). But I think most studies now use field knowledge, old maps and GIS to produce map proposals at biome level. The first "biome" map produced to Brazil in the XIX century by Martius is surprisingly similar to the current biome officially used in the country, showing that many times, what we are doing now is to refine with extra technology proposals made decades ago.