Gilbert has also decided to leave the orchestra, which he has led since the 1999-2000 season, after the contract expires.
He conducted the RSPO in its BBC Proms debut in 2004 and tours to Japan and New York.
"I find great joy in making music with the Royal Stockholm Philharmonic Orchestra and I am very proud of what we have achieved," Gilbert said in a statement. "It's exciting and important that our relationship is still maturing, and we continuously strive to deepen our communication and expressive capabilities."
The 37-year-old Gilbert is the son of two New York Philharmonic musicians. Since beginning his tenure in Stockholm, he has been named principal guest conductor of Hamburg's NDR Symphony and the music director of the Santa Fe Opera.
"We are extremely happy that Alan Gilbert has chosen to stay another period with the orchestra," RSPO director Stefan Forsberg said. "We are fully aware of the fact that Gilbert's career has rapidly evolved and we know that great interest is paid towards him in the international music community."