The company said in a statement that Kamprad "passed away peacefully surrounded by his loved ones" at his home in the southern Swedish region of Smaland on Saturday "following a brief illness".
"His legacy will be admired for many years to come and his vision - to create a better everyday life for the many people - will continue to guide and inspire us," Jesper Brodin, CEO and president of the Ikea Group, said in the statement.
Born in 1926 to a farming family in the southern Swedish region of Smaland, Kamprad founded the company at age 17.
Despite his enormous success and wealth, Kamprad's modest spending habits bordered on the obsessive.
The founder of IKEA and one of the greatest entrepreneurs of the 20th century, Ingvar Kamprad, has passed away at the age of 91. pic.twitter.com/DxyALH1LQ9- IKEA Today (@IKEAtoday) January 28, 2018
In 1973 he fled Sweden's higher tax structure for Denmark before seeking even lower taxes in Switzerland.
Starting in 2010 Kamprad gradually made way at the helm of the company for his three sons, finally returning to live in Sweden in 2014.
Kamprad announced in 2013 that he would be stepping down from the board of Inter Ikea, owner of the furniture giant's concept and brand, and his youngest son became chairman.
Last year, the European Commission announced that it had launched an investigation into Ikea's tax deals in the Netherlands.
The group insists that it complies fully with national and international tax regulations.
Sweden was neutral in World War II, and its Nazi party remained active after 1945. The Ikea founder said he stopped attending its meetings in 1948.