The 21-year-old has been in great form for the Bhoys this season, prompting speculation that he may be set for a move to the Premier League in the summer.
But Wanyama says he plans to remain with the Glasgow club and is targeting a domestic treble.
"I love it here at Celtic so I'll be here next season," he said. "I still have a contract with Celtic and I'm happy at the club, so I think I'll still be here.
"We want to do better than this season so, if we can get the treble next season, it will be a very good achievement for me.
"That's my dream for next season. Also, playing in the Champions League again."
PFA nomination for Wanyama
Wanyama made his announcement after learning he had been nominated for PFA Scotland's young player of the year award.
"It means a lot to me," he said. "I've had a good season.
"I'm very grateful and I want to thank my team-mates for giving me the chance to be here.
"For me, as a player, I believe that football is a game of learning. The more you play, the more you learn."
Wanyama is the only Celtic player to have been nominated for either of the two main PFA awards.
And he added: "I'm very surprised because, looking at my team-mates, they have had a very good season and the team has had a good season.
"There are a lot of players individually who have had a very good season and I'm just gutted that they're not here with me."