The campaign has been in place for eight months, with the city commencing curbside collection service three months ago, Knoxville said in a news release.
About 16,500 households have been using the biweekly service since October, recycling more than 1,200 tons of material.
Knoxville will deliver a second round of carts in mid-February for those who signed up after the initial Aug. 14 deadline, bringing the total to 20,000 households.
"We are very pleased with the response of our citizens to this program," said David Brace, Knoxville director of public service. "With 20,000 sign-ups, that means that one-third of the city's households are participating.
"We would like to expand the program at some point in the future if there is sufficient interest and funding to do so," he added.
With the 20,000 goal reached, enrollment in the program is closed for now. Residents who haven’t signed up yet can go on a waiting list to gauge interest through the city's web site or by calling 311.
More than 8,100 of the participating households have signed up for an incentives program with Recyclebank. About 2,500 rewards have been requested.