Let $X$ be a Fano variety over a number field. An Arakelov system of $v$-adic metrics on the anticanonical line bundle on $X$ gives rise to a height function on the set of rational points and to a new kind of adelic measures on the universal torsors over $X$. The aim of the paper is to relate the asymptotic growth of the number of rational points of bounded height on $X$ to volumes of adelic spaces corresponding to the universal torsors over $X$.