Poyet became the first Uruguayan to manage in England's top flight when he took over at Sunderland in 2013, and was most recently in charge of the Greece national team until March this year.
The 57-year-old will be tasked with reviving the fortunes of Jeonbuk, who have won the South Korean title a record nine times but have struggled in recent years.
They avoided relegation from the K League top flight in a playoff earlier this month after finishing 10th in the 12-team table.
Poyet starred for Chelsea and Tottenham during his playing career and got his first managerial job with Brighton in England's third tier in 2009.
He has also managed clubs in Greece, Spain, China, Chile and France.
Poyet's former Chelsea team-mate Dan Petrescu also managed Jeonbuk, leaving the job in April this year.
