The paper examines the potential role of sovereign wealth funds (SWFs) in implementation of the UN-initiated 2030 Agenda for Sustainable Development, in particular; the Sustainable Development Goals relating to combining long-term growth of global economy with protection of the Earth's environment, i.e. the creation of low-carbon (colloquially "green") economy. By definition, such a transition is highly capital-intensive, thus demanding mobilization of all available sources of financing. SWFs as state-run investment vehicles are among the most prospective ones. In recent decade, they noticeably strengthened their role in the world economy. SWFs proved to be the fastest growing group of institutional investors. Their cumulative AUM was estimated at around 7.4 Billion US dollars as of early 2018. By now, the world's leading SWFs from Norway, China, Singapore, Persian Gulf and some other states evolved into full-fledged market-driven investors with an active portfolio management strategy. In the conditions of current economic and geo-political turbulence SWFs show growing interest to the opportunities of "green" financing while seeking for viable alternatives to the increasingly fading traditional fixed-income instruments. However, the scale of SWFs' involvement in the creation of global "green" economy is still rather tiny as compared to the needs of respective investments, the activities of private business, as well as to the state funds' own financial capabilities. While considering the reasons of current situation and the prospects of its improvement the author argues that a massive "greening" of SWFs' investment strategies can (and should) be triggered by powerful political push from the respective national governments, namely, by major legal re-formatting of their mandates in the light of the Sustainable Development Goals. It can be expected that, with such push in place, in the upcoming years the state investment vehicles may change the rules, as well as the whole landscape, of the global "green "financing system.