Sir James, who was born in the small town of Minnigaff in Dumfries and Galloway, went on to teach economics at both Oxford and Cambridge universities.
The 82-year-old, who jointly won the Nobel prize in economic sciences in 1996, will be remembered for his “great intellect” and “wonderfully dry sense of humour”, the Scottish First Minister said.
Ms Sturgeon also told how Sir James, who studied at Edinburgh University, was also proud of his Scottish heritage.
Scottish Deputy First Minister and former finance secretary John Swinney described him as a “wise, gentle and deeply thoughtful man”.
Sir James won his Nobel prize for work on how to devise an optimal income tax regime, balancing both efficiency and equity, sharing the honour with William Vickrey of Columbia University.
During his career he served as the Edgeworth Professor of Economics and Fellow of Nuffield College in Oxford from 1968 to 1995 before becoming Professor of Political Economy at Cambridge in 1995.
In 2002 he was also appointed Distinguished Professor-at-Large at The Chinese University of Hong Kong.
He joined the Scottish Government’s council of economic advisers when it was established after the SNP came to power at Holyrood in 2007.
Ms Sturgeon said: “Sir James Mirrlees, who passed away earlier this week, will be sadly missed.
“His contribution to economics, in which he was awarded the Nobel prize in 1986, will leave a lasting legacy.
“I had the pleasure to get to know Jim personally through his valuable contributions to the Scottish Government’s Council of Economic Advisers, which he was a member of since 2007.
“Like many people of great intellect, Jim had a way of conveying the essence of any economic issue in a manner which was clear, thoughtful and accessible. He had a wonderfully dry sense of humour and served on the council with distinction throughout this period.
“Jim was also proud of his Scottish heritage. Born in the South of Scotland and having begun his studies at Edinburgh University, he always enjoyed returning to Scotland and sharing his wisdom, insights and knowledge.
“I am sure there will be further opportunities to celebrate the contribution of Jim’s legacy, which is recognised internationally. But at this time, my thoughts and wishes are with Jim’s immediate family amid their sad loss.”
Sir James is survived by his widow Patricia, his two daughters Catriona and Fiona from his first marriage to Gill, who died in 1993, and by his stepson Rory and four grandchildren.