The city "shared public safety concerns with the operator, and those concerns are shared by the operator," Mike Lyster, an Anaheim spokesman, said in a statement.
"As a city we respect free speech but also have a duty to call out speech that does not reflect our city and its values," Lyster added.
The event had previously been scheduled -- and later canceled -- at two other venues, in Orange and Riverside counties.
The rally was canceled at the Pacific Hills Banquet & Event Center in Laguna Hills because "we just want to stay clear of that,'' general manager Javad Mirtavoosi told the Orange County Register last week.
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It was then moved to the Riverside Convention Center, but officials with the Raincross Hospitality Corp., which manages and operates the city-owned center under contract with the city, informed city officials Friday night that the event would not take place.
"I recognize this was a divisive issue in our community, and I am glad it has been resolved,'' Mayor Patricia Lock Dawson said. "I commend Raincross Hospitality Corp. for this decision.''
Gaetz later announced an impromptu "peaceful protest'' against communism Saturday night at Riverside City Hall that would also feature Greene.
"I'm inviting all of my fellow patriots to join me and Marjorie Taylor Greene here tonight, 5 p.m. We're having a peaceful protest against communism,'' Gaetz said in a 2 p.m. video tweeted from outside Riverside City Hall at 3900 Main St.
"These folks, they try to cancel our venues, but they can never cancel our patriotism or our American spirit,'' added Gaetz, dressed in jeans and dark sunglasses. "Come tonight, 5 p.m., protected, First Amendment speech. I can't wait to see all my fellow patriots at the Riverside City Hall -- they'll hear us all throughout Southern California.''
Gaetz suggested Saturday that he and Greene might file a lawsuit over the Riverside cancellation.
The two Republican members of Congress are both strong supporters of former President Donald Trump.
"Radical communists have spent the last week trying to cancel our America First Rally w/@mattgaetz. Violent threats from BLM/Antifa were used again today to bully another venue. We won't back down. Our rally is happening tomorrow night in California,'' Greene tweeted Friday night.
The tweet was accompanied by a short video in which Green said, "The radical left and the woke mob is trying to cancel our rally but we're not gonna let it happen, so here's the message for you, communists Democrats: We are going stand up and we will have our America First rally tomorrow. You can't cancel us, you can't stop us. We're going to save America.''
City News Service contributed to this report.