From this paper we find the quote:
Lemma 1 (Petersen ) Every $2r$-regular graph can be decomposed into $r$ disjoint $2$-factors.
They described it as "Petersen’s classic decomposition theorem about regular graphs of even degree". The reference  is:
J. Petersen, Die Theorie der Regularen Graphen, Acta Math. 15 (1891), 193-220.
I don't have access to this paper, nor would I think it would do me much good, since the title suggests it's not in English.
Question: Where else can I find an English language proof of this result?