The 33-year-old former Bayern Leverkusen, Tottenham Hotspur and Manchester United forward joined the Ligue 1 club from Fulham in January and scored nine goals in 14 appearances.
"With AS Monaco, Dimitar showed all of his talent," Monaco vice president Vadim Vasilyev said in a statement.
"He is a great player and we are very proud to have him for the next season."
Big-spending Monaco finished second in Ligue 1 behind Paris St Germain.
(Writing by Ed Osmond in London, editing by Justin Palmer)
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