The 20-year-old has agreed a five-year contract with Monaco who are owned by Russian billionaire Dmitry Rybolovlev and have spent more than 170 million euros (£145 million) since the end of last season.
"The midfielder will continue his development with Monaco," the principality club said on their website.
Monaco, promoted to Ligue 1 for this season, have signed big names including Colombia striker Radamel Falcao from Atletico Madrid, and his fellow countryman James Rodriguez and Joao Moutinho of Portugal, both from Porto.
Kondogbia, a versatile midfielder with excellent passing skills, made an immediate impact at Sevilla and played 31 league games after joining for 3.5 million euros (£3 million) from French second division club Lens a year ago.
He won the Under-20 World Cup this year and has been called up by France for next month's World Cup qualifiers in Georgia and Belarus, after making his international debut in this month's friendly in Belgium.