Mauricio Pochettino says no decision has yet been made over striker Emmanuel Adebayor's future at White Hart Lane.
Craig Morgan and Ben Pringle have rejected new contracts at Rotherham and will leave the club on free transfers.
The 49-year-old tactician's deal was due to expire at the end of the current season but the former Holland international has now agreed to extend his stay at De Kuip.
He told the club website: "I have already said more than once that I am very happy at Feyenoord.
"The club has also stated on several occasions that they wanted to continue with me, so there wasn't much to discuss."
Koeman took control of Feyenoord at the start of the 2011-12 season and guided the Rotterdam club to a second-placed finish.
Club technical director Martin van Geel added: "From the start, it was clear we and Ronald had the same thing in mind - a contract extension of one year.
"If you both want that and also think the same about good conditions for both sides, then things can be quick."
The Dutchman began his managerial career with Vitesse Arnhem in 1999, before spending time with Ajax, Benfica, PSV Eindhoven, Valencia and AZ Alkmaar.