Asset Irgaliyev was born in 1986 in Kostanay. In 2008 he graduated from the Kazakhstan Institute of Management, Economics and Forecasting, the International Business School in Sweden, in 2009 — the University of York and in 2010 — the University of Nottingham with a degree in economy. He speaks Kazakh, Russian, English and German.
He started his career in September 2010 as a regional analyst for economic policy in Eastern Europe and the Caucasus in the economic department of the European Bank for Reconstruction and Development in London. From October 2011 to November 2012 he worked as the chief regional analyst in the same department. In November 2011 he became regional economist of the bank.
In January 2013, he was appointed director of the Center for Entrepreneurship Development of the Institute for Economic Research JSC. There Irgaliyev worked as a vice president, deputy chairman of the board, first deputy chairman of the board until early 2016. In February 2016 he was appointed chairman of the board of Institute for Economic Research JSC.
From October 2016 he served as adviser to the chairman of the Board of JSC Baiterek NMH, and in December 2016 he was appointed adviser to the Prime Minister of Kazakhstan.
From July 2018 to the present appointment, Irgaliyev worked as head of the Project Management Center of the Office of the Prime Minister of the Republic of Kazakhstan.