About 30 family and friends, including aunt Jessica Simpson, arrived around 12:30 p.m. on Saturday for a bounce house, cake, the singing of "Happy Birthday" and a surprise appearance by the cartoon character.
Wentz, 30, told PEOPLE last week that Bronx "likes Bob and he likes guitar – which he calls 'itar,' so we're going to have a SpongeBob party for him."
The party went well, according to Wentz, who thanked party planner Mindy Weiss and others on his Twitter page Saturday night for the "rad b-day for bronx."
Bronx's actual birthday was Friday, and the night before, mom Ashlee and aunt Jessica Tweeted their birthday wishes. Ashlee wrote, "BX's 1st bday tomorrow! My angel is going to be a year!! The greatest year of my life :)"
Jessica added, "Happy Birthday to my precious angel on earth!!! Bronx is 1 today!! I LOVE HIM SO MUCH!!! I can't believe it has been a year already."