What natural preservative to use to prepare homemade tomato paste for a 2 year shelf life?
I regularly make passata (tomato puree) home, and use a simple hot bath sterilisation (instructions below). I can usually keep it for about a year, but the result is not consistent and not 100% reliable: every 20 bottles I make, one leaks and gets spoiled. There are more sophisticated sterilisation methods that use a pressure pan (similar to an autoclave in the lab). Both of these methods rely on killing the bacteria naturally present in the preparation as well as in the residual air inside the can / jar.

However, as pointed by @Jefromi none of these techniques are 100% reliable for home preparation.

To be certain, you should use an acidity regulator. Lowering the pH of your sauce will prevent 
a big class of bacterias to develop. A cheap option which is commonly used in the industry is citric acid, which you might find in supermarkets and surely in brewing shops. If not available, you could also use vinagre or lemmon juice (less ideal). In any case, note that acidity alone will not do the job. Always use together with sterilization. 

For a reference, see this link for tomatoes in general, and this one for tomato paste specifically (thanks @Jefromi for these references).



Simpler water sterilisation process:


Before putting your mix in the jars, wash them carefully with hot water and soap.
After they have been filed, put your jars in a large pan.
(optional) Put a towel between the jars to avoid them hitting each other.
Pour water until the jars are completely covered.
Bring to boil. Low the fire so boiling is not violent. Boil for 30 minutes minimum.
Remove the jars and leave them to cool with the lid down. Turn them once cooled.


For this to work well, you need to be sure the lids are tight and no air can enter/scape. Be attentive to any leakage and use good jars.