The inspirational Dutchman, who was a free transfer signing from Sampdoria last summer, intends to complete the remaining year of his contract.
"I will be staying," the 33-year-old Gullit said. "Chelsea want to continue playing the way we played this year. I will play as long as I enjoy it. That is my priority."
He also backed Hoddle's decision. "It a great opportunity which does not come very often. I'm happy for him as a person, even though it's a bit sad for Chelsea. If he had been going to another club, it would have been different. It will be difficult because he will not be involved on a day-to-day basis.
"For me, it is also important that he is an independent person. He doesn't depend on what others might say."
Although Gullit will not be leaving Chelsea, others might. Peter Shreeves, the assistant manager, and the rest of Hoddle's backroom staff are all out of contract at the end of the month.
If the club decide against appointing Gullit, George Graham is likely to be one of the leading contenders for the job when his FA ban expires this summer.
Nigel Spackman, a senior Chelsea player, urged the Chelsea directors to look for a replacement who would use the same tactics as Hoddle.
He said: "It's important for Chelsea to find someone who can carry on the same style that Glenn has got us playing, just as it was vital for England to find someone who could take over from Terry Venables.
"We've got used to playing the way Glenn wanted and it was proving very successful, so it would be a great shame if the new manager went back to a 4-4-2 formation."
Colin Hutchinson, Chelsea's managing director, was "delighted for Glenn" but described his departure as a sad day for Chelsea. "It is a very emotional time," he said. "He has been an absolute joy to work with and we're all a bit down."Reuse content